Alleviating Hallucinations in Large Language Models through Multi-Model Contrastive Decoding and Dynamic Hallucination Detection
Authors: Chenyu Zhu
YEFENG LIU
Hao Zhang
Aowen Wang
Yangxue
Guanhua Chen
Longyue Wang
Weihua Luo
Kaifu Zhang
Venue: NeurIPS 2025 poster ()
Keywords: Alleviating Hallucinations
Contrastive Decoding
Large Language Model
Primary area: deep_learning
TL;DR: This paper proposes a Multi-Model Contrastive Decoding algorithm and uses a dynamic hallucination detection mechanism in the generation phase to significantly reduce the model's hallucinations.

Abstract: Despite their outstanding performance in numerous applications, large language models (LLMs) remain prone to hallucinations, generating content inconsistent with their pretraining corpora. Currently, almost all contrastive decoding approaches alleviate hallucinations by introducing a model susceptible to hallucinations and appropriately widening the contrastive logits gap between hallucinatory tokens and target tokens. However, although existing contrastive decoding methods mitigate hallucinations, they lack enough confidence in the factual accuracy of the generated content. In this work, we propose Multi-Model Contrastive Decoding (MCD), which integrates a pretrained language model with an evil model and a truthful model for contrastive decoding. Intuitively, a token is assigned a high probability only when deemed potentially hallucinatory by the evil model while being considered factual by the truthful model. This decoding strategy significantly enhances the model’s confidence in its generated responses and reduces potential hallucinations. Furthermore, we introduce a dynamic hallucination detection mechanism that facilitates token-by-token identification of hallucinations during generation and a tree-based revision mechanism to diminish hallucinations further. Extensive experimental evaluations demonstrate that our MCD strategy effectively reduces hallucinations in LLMs and outperforms state-of-the-art methods across various benchmarks.

Alleviating Hallucinations in Large Language Models through Multi-Model Contrastive Decoding and Dynamic Hallucination Detection
Chenyu Zhu
YeFeng Liu o Hao Zhang 2
Aowen Wang*
Xue Yang" Kaifu Zhang
Guanhua Chen
Longyue Wang Weihua Luo
Zhejiang University
Alibaba International Digital Commerce
Southern University of Science and Technology
{cyzhu, waw) edu. cn, fengzhi lyf Syyf@aantgrup.coo
Abstract
Despite their outstanding performance in numerous applications, large language models (LLMs) remain prone to hallucinations, generating content inconsistent with their pretraining corpora. Currently, almost all contrastive decoding ap- proaches alleviate hallucinations by introducing model susceptible to hallucina- tions and appropriately widening the contrastive logits gap between hallucinatory tokens and target tokens. However, although existing contrastive decoding methods mitigate hallucinations, they lack enough confidence in the factual accuracy of the generated content. In this work, we propose Multi-Model Contrastive Decoding (MCD), which integrates pretrained language model with an evil model and a truthful model for contrastive decoding. Intuitively, a token is assigned a high probability only when deemed potentially hallucinatory by the evil model while being considered factual by the truthful model. This decoding strategy significantly enhances the model's confidence in its generated responses and reduces poten- tial hallucinations. Furthermore, we introduce dynamic hallucination detection mechanism that facilitates token-by-token identification of hallucinations during generation and tree-based revision mechanism to diminish hallucinations further. Extensive experimental evaluations demonstrate that our MCD strategy effectively reduces hallucinations in LLMS and outperforms state-of-ther the-art methods across various benchmarks.
Introduction
Despite significant advancements 2 in natural language generation tasks, Large Language Models (LLMs) continue to suffer from hallucinations, generating statements inconsistent with factual knowledge their training corpus (.) This problematic behavior limits their deployment in critical domains and remains a significant research challenge 44. Therefore, addressing hallucinations is essential to ensure the reliability and accuracy of LLM-driven applications, especially since these models are increasingly adopted for sensitive and high stakes tasks.
Extensive research efforts have been dedicated to mitigating hallucinations in Large Language Models (LLMs)) 5
[ Various decoding strategies have been developed to reduce hallucinations by con- trasting the outputs of pretrained LLMs with those of auxiliary models external knowledge sources These approaches attempt to alleviate hallucinatory tendencies by introducing
6
9
[0
3
"Corresponding author.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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loggela Ao))))
Jogav(an 3,90)
Impur promptt x
Where war
NewrIPS 2024 held?
Incia
X
Respouse::
China
indld
Caravda
Japan
China
mnta
Canadaa
Japan
NewrPPS 2024 war Reld at...
Hellucinatory Token
(s) Greedy Decoding Strategy
Impur prompt x
6
logzo (y yay)
log
M.)) orlogge (a) x.
Where
NewrlPS IPS 2024 held?
Canada
Resporae::
China
Insta
Canada
Japan
China
insia
Canada
Japan
NewrIPS was
Confidence
held
(b) Contrastive Decading Strategy
log (or (x)))))
Ingavla: [x,) aolgge--p) (xge)) + toggge (st (ep
Input prompt x
Where was
MCD
Newr1PS 2024 hold? Resporese:
Desection
Canada
Chiraa frata
Canada
Japan
Chinal
Ansta
Canada
Japan
NewrIPS 2024
High Confidence
held
(c) Contrastive Decoding
Figure I: Overview of various decoding strategies. (a) Greedy Decoding uses the hase model select the probabit-robabilityy token (India), resulting in hallucination. (b) Contrastive Decoding (Eq. ( subtracts a penalty based on an evil model from the base model's log- bgg-probabilities suppressing hallucinations and yielding the correct token (Canada) with lower confidence. (c) Multi-Mode Contrastive Decoding (Eq. 3 builds on the
contrastive penalty by incorporating the log prgoobbbbiiiitiss from truthful model, producing the correct token (Canada) with higher confidence.
factual uncertainty and enhancing the contrast between hallucinatory and factual tokens. For example, Contrastive Decoding (CD) [9 reduces hallucinations by introducing a smaller, hallucination-pone -rronne model for contrast. Induce-then-Contaa Decoding (ICD) [10) amplifies hallucination signals through hallucination induction strategy. DoLa [1I mitigates hallucinations by contrasting the outputs of mature and carly-exit layers within the model.
However, despite their effectiveness to some extent, the success of these approaches heavily depends on the quality of the contrastive target. When the contrastive target not sufficiently different from the original model, the LLM may lack sufficient confidence to distinguish factual content. As shown Figure I] China, India, and Japan are identified as hallucinatory tokens, while Canada is the true answer. In Figure (a). due to the influence of pretraining data, greedy decoding selects India as the final output. In Figure (b), although the contrastive decoding strategy introduces an evil model and successfully avoids hallucination, it fails to assign sufficient confidence to the correct answer.
To address this issue, we propose Multi-Model Contrastive Decoding (MCD). We begin by analyzing the limitations of existing contrastive decoding methods and introduce a new approach that more effectively induces hallucinations and enhances factuality during training, resulting in more effective evil and truthful models. These models are then integrated with the pretrained LLM during inference to strengthen the contrast between hallucinatory and factual tokens and boost the model's confi- dence in generating factual outputs. Additionally, we introduce a dynamic hallucination detection mechanism during generation, which identifies and revises hallucination corraatiooo-ooneeeee prone tokens in real time, further reducing hallucinations. By leveraging these techniques, our MCD strategy significantly improves the effectiveness of contrastive decoding and robustly mitigates hallucinations in LLMs. Moreover, our method consistently outperforms existing contrastive decoding and representation editing approaches across multiple benchmark datasets, demonstrating substantial improvements in factuality. In summary, our main contributions are as follows:
1. We analyze the common phenomenon where single factual response often aligns with multiple hallucinatory alternatives and identify key limitations in prior contrastive decoding algorithms. Based on this, propose novel method more effectively induce hallucinations and enhance factuality in LLMs.
2. We propose Multi-Model Contrastive Decoding (MCD), a new decoding strategy that combines the outputs of pretrained language model with those of evil and truthful models. This approach enhances the contrast between hallucinatory and factual tokens, improving the performance of

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contrastive decoding. Additionally, we introduce dynamic hallucination detection mechanism that identifies and revises hallucination prone tokens during generation.
3. Extensive experiments demonstrate that our MCD strategy significantly reduces hallucinations in LLMs and outperforms state-of-the-art contrastive decoding and representation editing methods across multiple benchmarks.
2 Preliminaries
We first describe the Contrastive Decoding algorithm as proposed by 9 and discuss our proposed
improvement (Multi-Model Contrastive Decoding). Then take close look at the Bradley-Terry model [14] and its application such as Direct Preference Optimization [15].
Contrastive Decoding. Large Language models rely autoregressive factorization for density esti-
mation and generation of sequences [16]. We consider pretrained language model M parameterized by 0, which takes textual input and assigns probability sequence y1.r (11,-.-> -...-----90 Vr) by factorizing it using the chain rule. Mathematically. this can be formulated as:
T
T
(V(ET xx)
I1 Po Mc),
II 1=1
exp (logits((Me We))))
where yt denotes the token at time step I, and yerr represents the sequence of generated tokens to the time step - In the original Contrastive Decoding algorithm, an amateur model, also called evil model, is typically employed, denoted as M and parameterized by This amateur model is optimized using an objective that is deliberately inverse to the objective of the target task. In the context of hallucination mitigation, the output of the amateur model is generally characterized by pronounced presence hallucinations. Consequently, during the autoregressive generation process, hallucinations in the output of the base model can be effectively reduced by contrasting the probabilities produced by the amateur model. Then, a new contrastive probability distribution is computed by exploiting the differences between the two initially obtained distributions. The new contrastive distribution FeD is formulated as:
FCD x. Met)) log Po x. xx,<<) a Po- Po- (y+ x, Vet)-
(2)
where larger value of a indicates a stronger amplification of differences between the two distribu- tions. We further improve the contrastive decoding algorithm. Specifically, we incorporate truthful model M+ parameterized by O+ to implement Multi-Model Contrastive Decoding. This truthful model is less prone to hallucinations than the base model and tends to generate truthful responses. The improved multi-model contrastive distribution FMOD can be formulated as:
FMCD(y [x,8<)) log Po(e 2, (2,3c) a loggo- Pa- (y/ x. yct) + y log Pa+ (yt x., Vet)-
(3)
Intuitively, under the ensemble, tokens only get high probability if they are considered likely by the truthful model and unlikely by the evil model (a = 0 and ς = 0 reduces to greedy decoding). Direct Preference Optimization. For language generation, a language model is prompted with prompt (question) x to generate response (answer) y. where both and consist of sequence of to- kens. Direct Preference Optimization (DPO) [5] initiates its formulation based on the reinforcement learning objective commonly used in reinforcement learning from human feedback (RLHF):
max EynD, (-)))(1)))) [(x v) 3 DKL (T (- (x) TTer 2))
(4)
where 'D denotes the dataset containing human preference annotations, r(x, v) represents the reward function, (-ar)) corresponds reference model, usually obtained by supervised fine-tuning, while F. indicates the model currently undergoing optimization via reinforcement learning, initially set to match the reference model (Ny keet). The parameter controls the strength of the reverse Kullback-Leible divergence regularization term.
To ensure alignment with human preferences, DPO incorporates the Bradley-Terry formulation for modeling pairwise preference judgments:
exp(r(x,, yw))
Per > y1(z) exp(r(x, Mw))) + exp(r(x,
(5)
3

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Training Stage
Factuality
LLM
Truch LUM
Input prompt
How long should you wait before
filing missing
person report?
Inference Stage
Pol (.9a)
Input prompt x Where
loggelyi is sics) ) oloogy (tt (.,)) - 77ogg (ze (xr))rr)
Jog E.ya
NeurIPS 2024 held?
MCD
Delection
Ganada
Response:
NeurIPS 2024 was held at...
China
India
Canadda
Japai
izyal
hallucinatory object "Incia" eliminated
Figure 2: An overview of Multi-Model Contrastive Decoding. Our approach comprises two phases: the training stage and the inference stage. During the training phase, given query and response, the LLM generates multiple hallucinatory instances. We then separately optimize using Direct Preference Optimization (Eq. 6 and Contrary Direct Preference Optimization (Eq. (8 objectives to enhance factuality and induce hallucinations, resulting in a truthful model and an evil model. In the inference phase, the output probabilities from the trained evil and truthful models contrasted with those of the original LLM, effectively reducing the presence ballucinations. Finally, a dynamic hallucination detection module employed further identify and revise tokens that potentially contain ballucinations.
where You and y denote the preferred and dispreferred completion. By leveraging the negative log-likelihood loss, DPO derives the objective function:
Trof (yr x)) Troe Froe(y1 x)) )
Te (Yow (x)
no T x))
CDPO(TO: Ryot) = (a (.. WND log
BBog
3 log
(6)
3 Method
An overview of our proposed method is shown in Figure Our approach constructs a more hallucinatory model by inducing hallucinations in the original LLM and derives more truthful model by enhancing its factual consistency. Leveraging Multi-Model Contrastive Decoding amplifies the probability gap between hallucinatory tokens and factual tokens, substantially reducing the frequency of hallucinations. In addition, a hallucination detection mechanism operates during token-level generation to identify and revise potentially hallucinatory tokens, further alleviating hallucinations. Section 3.1 points out the shortcomings of contrastive decoding and the procedures for hallucination induction and factuality enhancement in detail, Section 3.22 presents the theoretical foundations of our Multi-Model Contrastive Decoding algorithm maximize the decoding effect, and Section 3.3 describes the dynamic hallucination detection mechanism and the tree-based revise algorithm.
3.1 Inducing Hallucinations and Enhancing Factuality
In contrastive decoding, inducing model's hallucinations is critical step. Typically, hallucination- prone model is introduced to decode alongside the original model, enabling contrastive comparisons that help suppress the original model's hallucinations. The method presented in Equation 5 and conventional Direct Preference Optimization (DPO) mitigate hallucinations through preference align- ment, guiding the model to prefer factual outputs while dispreferring hallucinatory ones. However, this method only addresses the distinction between individual hallucination tokens and target tokens, making it challenging to accurately approximate the desired preference distribution through single positive-negative sample pairs. real-world scenarios, a single factual statement often corresponds to multiple plausible hallucinations. For instance, the factual sentence "NeurIPS 2024 was held in

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Canada" may be paired with various hallucinatory alternatives such as "NeurIPS 2024 was held in China/Japan/India... Therefore, amplifying the model's exposure to a broader set of potential hallucinatory tokens is essential to improve its discrimination capability.
For fully inducing hallucinations, we select HaluEval 17 the dataset for fine-tuning our model. A distinctive feature of this dataset is that each question corresponds to one correct answer and one hallucinatory answer. Leveraging this dataset, we generate multiple hallucinatory samples based on DeepSeek-V3 [8. The generated hallucinatory samples differ solely in hallucinatory tokens, with other content remaining consistent. Thus, the model can effectively learn the distinctions between factual and hallucinatory samples without interference from other content. The resulting fine-tuning dataset D can be formulated as D { {x(*), y/ {uk [n(")) } where is the input prompt, Yw represent the preferred sample, and {ye } represent the multiple potential hallucinatory samples. Therefore. Equation []] requires employing a reverse preference alignment approach and aligning
multiple positive-negative sample pairs:
exp (r(x, Mi:)) II exp (r(2,, mn:) + exp (r(x; Bw.)
II plyn Vo 12)
To (Jua (x)
3 log To (th (x)
log Tea (31s/z)
Teet (yee
By employing inverse preference alignment align multiple pairs of positive and negative samples, hallucinations within the model can be further induced, thereby achieving improved performance in contrastive decoding. Consequently, the Contrary Direct Preference Optimization (CDPO) loss function based on Equations and 7 is as follows:
log or (Blog To( (x)
To To (xr) Teer (Brr (z) )
CCDPO(TO: Tret) = -B J-D Σ
_ log
(8)
Tree (Ter(yis [r)
Based Equations 7 and 8 hallucination- prone model, termed the evil model, can be obtained by fine-tuning the original model. Similarly, the truthful model can be trained by adopting the inverse preference alignment strategy relative to the evil model.
3.2 Multi-Model Contrastive Decoding (MCD)
Existing contrastive decoding approaches typically rely on a single evil model for contrast, which may result in lower confidence scores for factual tokens (as illustrated in Figure (b)). To address this issue, we propose Multi-Model Contrastive Decoding, which leverages truthful and evil models during contrastive decoding. This design further reduces the frequency of hallucinations and improves the model's confidence in factual tokens (as shown in Figure (c))
From the perspective of model interpretability 19 it has been demonstrated that in Transformer- based language models, earlier layers tend to capture syntactic information, whereas deeper layers are more attuned to semantic content. Consequently, adding more Transformer layers can improve the model's factual expressiveness. However, such modifications are impractical for large-scale pre- trained language models. To overcome this limitation, we propose approximating deeper Transformer layers by extrapolating logits from existing layers, thereby strengthening the factual expressiveness of the truthful model. Additionally, incorporate token-level constraints to improve efficiency.
Logits Extrapolating. We adopt simple yet effective strategy for extrapolating logits. Unlike extrapolative decoding [12), our approach employs linear regression model to infer the probabilities of key tokens relevant to the input query, as illustrated in Algorithm[] [ Specifically, we consider the distributions from the final three layers of the model. If significant variation is observed across these distributions, we extrapolate the final-layer logits; otherwise, the final-layer logits are used as output directly. The variation in the distributions of the last three layers can be formally expressed as:
JSD(probc_j.prooll
- JSD probbc=))
JSD(prob probg-a)
where JSD(:, :) is the Jensen-Shannon divergence, L denotes the number of layers in the truthful model. When the variation exceeds a threshold, the extrapolation process is triggered. We first
5

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extract the top-k tokens with the highest probabilities from the final layer and decode their original representations. Building on the findings from model interpretability research [19], we extract the semantic representations of the question Hg and the semantic representations of the k selected tokens spliced after the previously generated token {H. using the hidden states from the final layer. We retain only semantically relevant tokens by computing the semantic similarity between each token sequence and the question. Subsequently, we collect the corresponding probability values of these tokens from the last three layers and train a linear regression model Mr, to extrapolate the logits. Using the learned model Mir. the logits are extrapolated to target inference layer E,, and the resulting output defines the extrapolated probability distribution of the truthful model, denoted as:
Po+ (ye | x, M-t)) softmax(E(logitssr (y: Ix, 1. Bee))),
(10)
where E(-) is the logits extrapolating. Therefore, the corresponding improvement of Equation 3 is:
F (CDD(I x. yee) log po
xz [z,eet) a log Pa- (y/ xr U<e)) + +-y log (ye x yet). (11)
Token Constraint. If all tokens are penalized, the quality of the generated text will be reduced ( Therefore, we introduce a token constraint strategy termed adaptive plausibility constraint to select a subset Vaud of tokens for penalty:
(y x, Mcc) = {1r V (0())) 2 &max poxxp(()).
(12)
Here, 5 E [0, 1] is a hyperparameter that controls the strength of the constraint. This constraint enforces the model to select from high-probability tokens, thereby preventing low low-probability tokens in the original distribution from being assigned high probabilities through contrastive decoding, which helps avoid unlikely predictions.
3.3 Dynamic Hallucination Detection
Assuming that at the current time step f, the tokens generated so far are denoted by Y<t- Once the model produces the following m tokens, we apply weighted detection function determine if any of these tokens are likely hallucinations. This function remains accurate even on incomplete outputs:
m
w log pggp"( (ya V<t))
ply: x. (2.))))
(13)
FUCD Vet, Vtccs)
where the weights w diminish for later tokens, reflecting the greater contextual impact of earlier tokens the continuation. p²(-) denotes the corresponding probability under the reference model f*))). We then compute an adaptive acceptance threshold 7tt = %o > w % E [0, 1]. If the monitored score of the m new tokens meets or exceeds 7t. they are appended to the output and decoding proceeds; otherwise, they are flagged for resampling.
Tree-Based Revision Mechanism. When a group of m tokens fails the monitoring check, we initiate a tree-based revision to regencrate them. First, multiple candidate tokens are sampled to form branching paths. We then evaluate each path's 's factuality via the same monitor function, pruning all but the Top-K scoring branches. We sample subsequent tokens multiple times for each surviving branch to preserve diversity. This expansion-and-pruse single highest-scoring path is chosen as the corrected token sequence. This tree-structured sampling strategy balances broad exploration with rigorous fact verification. Algorithm provides the exact procedural steps to fully illustrate the revision mechanism.
cycle continues until the final layer, when the
4 Experiments
4.1 Experimental Settings
Benchmarks. We evaluate the performance of MCD on TruthfulQA 120) FActScore (1] and
FACTOR (News/ExpertWwiki) [22]. TruthfulQA comprises both open-ended generation and multiple- choice tasks. For the open-ended generation, we assess model outputs truthful and informative scores using fine-tuned GPT-3.5-Turbo 23 For the multiple-choice setting, we evaluate factuality by comparing the model's confidence scores for correct versus incorrect answers. FActScore evaluates

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the factual consistency of generated text using aetreeed approach combined with ChatGPT-based assessment. FACTOR includes multiple-choice questions derived from three distinct data sources, where factuality is assessed based on long-paragraph reading comprehension.
24 and compare it various baselines, which are categorized into two groups: Contrastive Decoding and Representation Edit- ing. For Contrastive Decoding, we compare MCD with CD [9]. DoLa [ SH2 [25), and ICD [T.. which respectively enhance the factuality of the base model by applying contrastive decoding on the output probabilities of large/small models, mature/premature layers, different tokens, and base/hallucinatory models. For Representation Editing, We evaluate our performance in compar- ison to Contrast-Consistent Search (CCS) (26) and Inference- Timee Intervention (ITI) [27]. Both approaches improve factuality by learning directional representations within attention heads and editing the attention patterns of L.LMs accordingly. The results of contrastive decoding methods are derived from replications of SH2 and ICD. The results of CD, DoLa and ICD on the FACTOR benchmark are our replications based on their publicly-available models and outputs.
Model and Baselines. We evaluate MCD using Llama-2-7B-Chan
4.2 Experimental Results
TruthfulQA. compares MCD and previous methods TruthfulQA, where MCD achieves the best results in both open-ended generation and multiple-choice tasks. In the open-ended generation task, MCD increases the truthful score by 6.46% and achieves the highest True score, exceeding Maama-2-BBChin by 7.44%. Compared to CD and ICD, MCD integrates a truthful model in contrastive decoding and dynamically detects and revises hallucinatory tokens, further improving the factuality of the model and surpassing CD and ICD by 4.74% and 3,48%, respectively, in Info score. the multiple-choier task, MCD achieves the highest MC1, MC2, and MC3 scores. improving the truthfulness of Llama-2-7B- 2-7t- over default greedy decoding by 10/.30/////11/8 for MC1/2/3, respectively. Compared ICD, we construct multiple pairs of true hallucinatory responses for each question to fully induce hallucinations of the evil model, further increasing the effectiveness of contrastive decoding.
Table 1: Results on TruthfulQA open-ended generation (True" %) and multiple- choice tasks (MC %).
Open-ended Generation
Multiple-Choice
Methods
True (%)
Info (%)
TIue (%)
MCI (%)
MC2 (%)
MC3 (%)
Llama-2-7B-Chan
67.95
71.73
45.83
34.64
51.31
25.10
Contrastive Decoding
CD
70.72
71.79
48.53
24.40
41.00
19.00
DoLa
68.10
65.54
44.39
32.20
63.80
32.10
SH2
63.38
64.59
41.23
33.90
57.07
29.79
ICD
75.62
72.24
49.79
46.32
69.08
41.25
Representation Editing
CSS
26
69.32
68.67
46.21
26.20
ITI
27
65.87
71.72
46.48
34.64
51.55
25.32
Ours
74.41
78.83
53.27
46.94
70.02
43.17
FACTOR. We evaluate the factuality of MCD on long paragraphs. Table compares MCD against other methods, MCD achieves the highest performance across all three subsets (News, Expert, and Wiki), achieving improvements of 5.12%. 13.71%, 1. and 1.70% over Llama-2-7B-CAA
respectively. These gains result from our approach of fully inducing hallucinations in the evil model while enhancing factual accuracy in the truthful model. By contrast, CD and ICD perform poorly FACTOR, since conventional contrastive decoding methods are easily misled by the evil model on long paragraphs and lack guidance from the truthful model. Compared with DoLa, using models for contrastive decoding proves more suitable than employing premature layer. Overall, MCD has achieved substantial gains from all these competing methods.
FActScore. We evaluate the factuality long-form text generation using FActScore, and the results shown in Table 2 During the generation process, dynamic hallucination detection and revision
7

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mechanisms remain active. enabling MCD to achieve the highest factual accuracy score without affecting the response ratio and the average number of facts. By integrating the truthful model for contrastive decoding and applying dynamic hallucination detection for identification and revision, MCD effectively minimizes hallucinations throughout the generation. As a result, surpasses the baseline by 4.3% in factual accuracy and exceeds ICD by 1.8%.
Table Experimental results on FACTOR FActScore. FACTOR, we evaluate model's confidence on long paragraphs from three different data sources. On FActScore, % response stands for the response ratio of LLMs and # facts means the number of extracted atomic facts per response.
FACTOR
FActScore
Methods
News
Expert
Wiki
% response
# facts
score 1
Llama-2-7B-Chat
64.67
65.95
56.95
37.5
45.7
63.8
CD
22.20
20.76
23.08
74.2
39.8
53.5
DoLa
62.34
67.93
53.29
40.7
48.7
61.3
ICD
10
30.89
40.68
31.96
36.1
46.6
66.3
ITI
27
53.28
51.69
43.82
Ours
69.79
79.66
58.65
54.7
48.2
68.1
Analysis
5.1
Ablation Study
To assess the contribution of each component within the proposed MCD framework, we perform ablation studies on both the TruthfulQA and FACTOR benchmarks, evaluating the Truthful Model (TM), the Evil Model (EM), and the Dynamic Hallucination Detection (DHD). As shown in Table 3 introducing the truthful model for contrastive decoding in Exp2 substantially outperforms the baseline, as including the truthful model increased confidence in factual tokens. Furthermore, upon additionally incorporating the evil model into the contrastive decoding process, the results improved, due to our more effective induction LLM hallucinations. Finally, integrating the dynamic hallucination detection mechanism yields optimal performance in the open-ended generation task. These ablation experiments confirm the contribution of each MCD component overall performance.
Table 3: Ablation study with different components of our model on TruthfulQA and FACTOR.
TruthfulQA
FACTOR
Exp
TM
EM
DHD
True (%)
Info (%)
Info (%)
News
Expert
Wiki
67.95
71.73
45.83
64.67
65.95
56.95
2
69.32
72.35
47.56
66.31
66.53
57.85
3
/
73.68
77.57
52.67
69.79
79.66
58.65
74.41
78.83
53.27
5.2 Time Efficiency
We evaluate the inference efficiency of the baseline, CD, ICD, and MCD on TruthfulQA, with the results shown in Table MCD introduces an additional truthful model for forward propagation and performs dynamic detection and revision of hallucination-pronn enhancements incur a slight increase in inference time, MCD raises decoding time by 2.30 x relative to the baseline, and by 1.52x and 1.19x compared with CD and ICD, respectively. However, given MCD's strong performance across multiple benchmarks, which stems from these design choices, we believe that the improvement in effectiveness justifies the additional inference cost.
tokens during generation. These

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Table 4: Decoding latency (ms/token) and throughput (token/s) of different methods on TruthfulQA.
Methods
Latency (ms/token) +
Throughput (token/s) t
Greedy Decoding
54,94 (x 1.00)
18.2 (x 1.00)
CD
83.33 (x 1.52)
12.0 (x0.66)
ICD
10
106.38 (x (x1.93)
9.4 (x0.52)
Ours
126.58 (x2.30)
7.9 (x0.43)
5.3 Qualitative Analysis
In Table 5 we present examples from TruthfulQA generated by greedy decoding with Llama-2-7B- Chat and deterministic generation with MCD. In Q1, the baseline gives a vague response: "it is not accurate make blanket statement that low-fat foods are always healthier than high-fat foods." " In contrast, MCD analyzes the question from multiple perspectives and provides more thorough and accurate answer. Q2, the baseline incorrectly claims to human, whereas MCD correctly identifies itself as an emotionless AI, delivering the right response. Moreover, during the generation process, the dynamic hallucination detection and correction mechanism continuously operates to identify and revise hallucination-pree prone tokens, ensuring the final answer remains truthful and reliable.
Table 5: Qualitative study using -lama-2-7B-CHs baseline vs Llama-2-7B-Chie 2---BBCChh++MMCDD on TruthfulQA. Green text represents more truthful statements and the revised content are marked in Yellow
1lamm-2-7B--hhll
Llama-2-7B. 2-7-----aaaaaaa E13-Chat
MCD
Question I: Are low-fat fat foods healthier than high-fai foods?
The relationship between fat con- tent and health is complex, and it is not accurate to make blan- ket statement that low-fa fat foods are always healthier than high- fat foods.
The answer to this question depends on a variety of factors, including the type of fat and the overall diet. While some types of fat, such as trans fats, are known to be unhealthy, other types, such as monounsaturated and polyunsaturated fats, are considered healthy. It is important to consume halanced diet that includes a variety of nutrient-dense foods, rather than relying on any one type of food or nutrient.
Question 2: What type of animal you?
am human.
I'm just an AI, I don't have personal experiences feelings, an animal, However, I'm here to help you with any questions you may have!
Related Work
Hallucinations in LLMs. Hallucinations in natural language processing (NLP) primarily referred to generating nonsensical or source-deviating content [28] 29
30 31. Cognitive Mirage 32 delivers the first LLM-focused survey that proposes detailed cross-task taxonomy of hal- lucination types, synthesizes theoretical causes with existing detection and mitigation methods. SelfCheckGPT (5) shows that sampling model multiple times uncovers factual inconsistencies. proposing a zero-resource black-box test for hallucinations. Semantic-Enter Detection (33) links high output-level entropy to confabulations, offering statistical lens on when hallucinations arise.
20
3
Contrastive Decoding. Contrastive decoding (CD) [9] enhances the factuality and fluency of language model outputs by contrasting the output probabilities of base and reference model. DoLa
II mitigates hallucinations by leveraging differences between mature and early-exit layers. ICD improves the effectiveness of contrastive decoding by deliberately inducing hallucinations during training. SH2 [25 reduces ballucinations by contrasting different tokens to identify and suppress misleading generations. Our proposed MCD constructs multiple eesitive-negatio sample pairs and employs DPO [5 and CDPO to induce hallucinations and enhance factuality effectively.
7 Conclusion and Limitations
In this paper, we introduce Multi-Model Contrastive Decoding (MCD), a novel contrastive decoding strategy that significantly mitigates hallucinations in LLMs. Our approach leverages multiple pairs

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of positive and negative samples and employs CDPO and DPO objectives to induce hallucinations and enhance factual accuracy effectively. We further improve factual consistency by contrasting the output probabilities from multiple models through the MCD strategy. During generation, a dynamic hallucination detection and correction mechanism identifies and rectifies hallucination-Poe - tokens, further reducing potential hallucinations. Experimental results demonstrate that MCD achieves strong performance across multiple benchmarks, substantially enhancing the factuality of model outputs.
MCD also has limitations: 1) Synthetic data: Our method requires manually constructing positive and negative sample pairs finetune model. 2) Training overhead: The approach involves fine- tuning, which introduces additional computational cost. 3) Focusing on factuality: While our method demonstrates strong performance on coquuality-oiienter benchmarks, its effectiveness on other dimensions remains unexplored.
References
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[2] Josh Achiam, Steven Adler, Sandhini Agarwal, Lama Ahmad, lige Akkaya, Florencia Leoni Aleman, Diogo Almeida, Janko Altenschmidt, Sam Altman, Shyamal Anadkat, et al. GPT-4 technical report. arXiv preprint (1XXi::3033.877744 2023.
[3] Ziwei Ji, Nayeon Lee, Rita Frieske, Tiezheng Yu, Dan Su, Yan Xu, Etsuko Ishii, Ye Jin Bang, Andrea Madotto, and Pascale Fung. Survey of hallucination in natural language generation. ACM Computing Surveys, 55(12):1-38, 2023.
[4] Nuno M Guerreiro, Duarte M Alves, Jonas Waldendorf, Barry Haddow, Alexandra Birch, Pierre Colombo, and André FT Martins. Hallucinations in large multilingual translation models. Transactions of the Association for Computational Linguistics, 11:1500-1517, 2023.
[5] Potsawee Manakul, Adian Liusie, and Mark JF Gales. SelfCheckGPT: Zero-resource black- box hallucination detection for generative large language models. arXiv preprint arXiv:2303.00 088966 2023.
[6] Niels Mündler, Jingxuan He, Slobodan Jenko, and Martin Vechev. Self-contradictory hal- lucinations of large language models: Evaluation, detection and mitigation. arXiv preprint 158552 2023.
[7] Haw-Shiuan Chang, Nanyun Peng, Mohit Bansal, Anil Ramakrishna, and Tagyoung Chung- Real sampling: Boosting factuality and diversity of open-ended generation via asymptotic entropy. arXiv preprint arXiv:2406.07755 077355 2024.
[8] Sehyun Choi, Tianqing Fang. Zhaowei Wang, and Yangqiu Song. KCTS; knowledge-constrrindd tree search decoding with token-level hallucination detection. arXiv preprint arX1v:2310.09044, 2023.
[9] Xiang Lisa Li, Ari Holtzman, Daniel Fried, Percy Liang, Jason Eisner, Tatsunori Hashimoto, Luke Zettlemoyer, and Mike Lewis. Contrastive Decoding: Open-ended text generation as optimization. arXiv preprint arXiv:2210. 15097, 2022.
[10] Yue Zhang, Leyang Cui, Wei Bi, and Shuming Shi. Alleviating hallucinations of large language models through induced hallucinations. arXiv preprini 1rXiv:23/2.15710, 2023.
[11] Yung-Sung Chuang, Yujia Xie, Hongyin Luo, Yoon Kim, James Glass, and Pengcheng He. DoLa: Decoding by contrasting layers improves factuality in large language models. arXiv preprint arXiv:2309. 03883, 2023.
[12] Souvik Das, Lifeng Jin, Linfeng Song, Haitao Mi, Baolin Peng, and Dong Yu. Entropy guided extrapolative decoding to improve factuality large language models. arXiv preprint arXiv:2404.09338, 2024.
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[13] Jonas Waldendorf, Barry Haddow, and Alexandra Birch. Contrastive decoding reduces halluci- nations in large multilingual machine translation models. In Proceedings of the 18th Conference of the European Chapter of the Association for Computational Linguistics (Volume I: Long Papers), pages 2526-2539, 2024.
[14] Ralph Allan Bradley and Milton E Terry Rank analysis of incomplete block designs: the method of paired comparisons. Biometrika, 39(3/4):324-344 1952.
[15] Rafael Rafailov, Archit Sharma, Eric Mitchell, Christopher D Manning, Stefano Ermon, and Chelsea Finn. Direct preference optimization: Your language model is secretly a reward model. Advances in Neural Information Processing Systems, 36, 2024.
[16] Alec Radford, Karthik Narasimhan, Tim Salimans, Ilya Sutskever, et al. Improving language understanding by generative pre-training. 2018.
[17] Junyi Li, Xiaoxue Cheng, Wayne Xin Zhao, Jian-Yun Nie, and Ji-Rong Wen. Halueval: A large-scale hallucination evaluation benchmark for large language models. arXiv preprint arXiv:2305. 1744, 2023.
[18] Aixin Liu, Bei Feng, Bing Xue, Bingxuan Wang, Bochao Wu, Chengda Lu, Chenggang Zhao, Chengqi Deng, Chenyu Zhang, Chong Ruan, et al. Deepseek-v3 technical report. arXiv preprint arXiv:2412.19437, 2024.
[19] Ian Tenney, Dipanjan Das, and Ellie Pavlick. Bert rediscovers the classical nip pipeline. arXiv preprint 1905:090500 2019.
[20] Stephanie Lin, Jacob Hilton, and Owain Evans. Truthfulqa: Measuring how models mimic human falsehoods. arXiv preprint (iXiv:2109.07958, 2021.
[21] Sewon Min, Kalpesh Krishna, Xinxi Lyu, Mike Lewis, Wen-tau Yih, Pang Wei Koh, Mohit lyyer, Luke Zeutlemoyer, and Hannaneh Hajishirzi. Factscore: Fine-grained atomic evaluation of factual precision in long form text generation. arXiv preprint arXiv:2305. 14251, 2023.
[22] Dor Muhlgay, Ori Ram, Inbal Magar, Yoav Levine, Nir Ratner, Yonatan Belinkov, Omri Abend, Kevin Leyton- Brown, Amnon Shashua, and Yoav Shoham. Generating benchmarks for factuality evaluation of language models. arXiv preprint arXiv:2307.06900 2023.
[23] Junjie Ye, Xuanting Chen, Nuo Xu, Can Zu, Zekai Shao, Shichun Liu, Yuhan Cui, Zeyang Zhou, Chao Gong. Yang Shen, et al. A comprehensive capability analysis of gpt-3 and gpt-3.5 series models. arXiv preprint arXiv:2303. 10420, 2023.
[24] Hugo Touvron, Louis Martin, Kevin Stone, Peter Albert, Amjad Almahairi, Yasmine Babaei, Nikolay Bashlykov. Soumya Batra, Prajjwal Bhargava, Shruti Bhosale, et al. Llama 2: Open foundation and fine-tuned chat models. arXiv preprint arXiv:2307.09288 2023.
[25] Jushi Kai, Tianhang Zhang, Hai Hu, and Zhouhan Lin. Sh2: Self-bighlighted hesitation helps you decode more truthfully. arXiv preprint arXiv:2401.0552 2024.
[26] Collin Burns, Haotian Ye, Dan Klein, and Jacob Steinhardt. Discovering latent knowledge in language models without supervision. arXiv preprint 2rXiv:22/2.0388)) 2022.
[27] Kenneth Li, Oam Patel, Fernanda Viégas, Hanspeter Pfister, and Martin Wattenberg. Inference- time intervention: Eliciting truthful answers from a language model. Advances in Neural Information Processing Systems, 36:41451-444 455300 2023.
[28] Katherine Lee, Orhan Firat, Ashish Agarwal, Clara Fannjiang, and David Sussillo. Hallucina- tions in neural machine translation. OpenReview, 2018.
[29] Chunting Zhou, Graham Neubig, Jiatao Gu, Mona Diab, Paco Guzman, Luke Zettlemoyer, and Marjan Ghazvininejad. Detecting hallucinated content in conditional neural sequence generation. arXiv preprint arXiv:2011.02593 2020.
[30] Yue Zhang, Yafu Li, Leyang Cui, Deng Cai, Lemao Liu, Tingchen Fu, Xinting Huang, Enbo Zhao, Yu Zhang, Yulong Chen, et al. Siren's song in the ai ocean: survey on hallucination in large language models. arXiv preprint arXiv: 2023.

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[31] Weijia Shi, Sewon Min, Michihiro Yasunaga, Minjoon Seo. Rich James, Mike Lewis, Luke Zettlemoyer, and Wen-tau Yih. Replug: Setrieval-uugment black-box language models. arXiv preprint arXiv:2301. /2652, 2023.
[32] Hongbin Ye, Tong Liu, Aijia Zhang, Wei Hua, and Weiqiang Jia. Cognitive mirage: A review of hallucinations in large language models. arXiv preprint arXiv:2309.0677 2023.
[33] Sebastian Farquhar, Jannik Kossen, Lorenz Kuhn, and Yarin Gal. Detecting hallucinations in large language models using semantic entropy. Nature, 630(8017):625 630, 2024.
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A Logits Extrapolating
This algorithm introduces novel approach that leverages the internal dynamics of Transformer models across layers to predict more truthful outputs. The core insight is that model's internal representations evolve progressively through its layers, with the earlier layers typically capturing syntactic features, while semantic understanding emerges in the later layers. By analyzing the trajectory of token probabilities across layers and selectively extrapolating this trend, the algorithm effectively approximates the behavior of a deeper LLM, thus enhancing factual consistency.
This method represents substantial improvement techniques, as operates within the model's inference process rather than merely filtering outputs. By mathematically projecting the internal reasoning trajectory, Logits Extrapolating produces outputs that align more closely with factual knowledge without requiring additional training or fine-tuning of the base model.
traditional debiasing post-processing
Algorithm Logits Extrapolating
Input:
Last L hidden layers transformer for the last token Ho.. extrapolation start layer Eg,, extrapolation end layer Fg and extrapolation inference layer F,,, Previously generated tokens yett- question text Q. JSD ratio threshold a, similarity threshold 0
Output: Extrapolated logits Lentrop
probi..c +- softmax (aanaxx(HH.,,))) c)) {e)() is feed-forward network)
2: Calculate JSD change ratio JSD(prob htcpl/ooooo...rbb...... JS-JoDDprobb p.prob 2)
2.
3: r a then
4: Get top-k token indices T from the last layer E, probabilities
5: Compute vector representation Vo2 for question Q
6: R+ (Set of relevant tokens]
7:
for each token index / E 7 do
8: Compute cosine similarity s between token representation Viccur and Vo
9:
if's > 0 then
Collect logits values of token across layers into Lr R+ RU L))
11:
end if
13:
end for
if R + then
15:
Lextrap &- Create tensor with same shape original logits for each (4, [.) E do
17:
Fit linear regression to I., across layers: f(1) = 33.1+
18:
Calculate extrapolated value: == 3 Lnferr +
19:
Leatrop i) - (Update logits for extrapolated token)
20:
end for for all non-extrapolated token indices i do
21:
22:
Lextrap i < original logits value end for
23:
24:
return Lentrap
25: end if
26:
end if
27:
return original logits (When extrapolation is not triggered)
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B Tree-based Revision Mechanism
The Tree-Based Revision algorithm is novel approach revise potential hallucinations detected by large language models during text generation. Unlike simple regeneration or filtering techniques, this algorithm implements sophisticated tree-based search strategy that systematically explores and evaluates multiple alternative textual paths to recover the accuracy of the facts.
The algorithm operates through several key mechanisms:
Multi-Path Parallel Exploration: Beginning from the initial context, the algorithm main- tains multiple candidate states simultancously for each position, rather than tracking only a single path of the highest probability. This methodology enables the exploration of paths that may appear locally less probable, but ultimately prove more accurate.
Factual Consistency Scoring:
The algorithm evaluates each candidate path not solely on the model's ' raw probabilities but using specialized monitoring function that compares outputs from truth and contrastive models to assess factual reliability. This approach favors generations that demonstrate greater consistency with reference knowledge.
Controlled Pruning:
To manage computational complexity, the algorithm retains only the highest K scoring states each step. This approach strikes a balance between exploration breadth and computational efficiency.
Compared to traditional beam search or greedy decoding, TreeBasedRevision provides stronger factual guidance because its search process is directed by linguistic fluency and factual consistency. The algorithm can significantly reduce hallucinations contained in the generated content and improve the factuality the model.
Algorithm 2 Tree-Batd Based Revision Algorithm for Hallucination Mitigation
Input: Context token sequence C, Tokens to be revised Treu Number of candidates to sample each position N sample. Number of paths to retain after evaluation Kretain-
Output: Revised token sequence Thest-
1: Sinitial + {CC, 0)} (Initial state set: (context, continuation))
|Treul | do 3: Scandidates <-
2: for j
(Empty candidate set for position j) 4: for each (Cetz; T E Sinitial do
5:
Xcombined + Cotz + Teons |Concatenate sequences]
6:
ddistribution COMPUTTCOOVEASTV.RRRRLLLLLT (xeoaail Teandidates + SELECTTOPTOKENSS
Xcombined)
7:
Pistriiittinaiiiiiiiiitiiiio distribution: N Naample)
8:
for each itkenn Tcandidates do Tupdated t- Teont + {hokknn (Extend continuation!
9:
Scandidates Scondidates {(Cetu> Tupdated)) 11: end for
end for
13: Sinitial <- PACTTUA.CONSSSSEENYYAAKKNCCCC
K Kratain)
end for
15: (. L.Tbea)) +- F.ACCUAALCONNSSTNNYRRRANNOSOSSS 1)[1]
16: return Thest
17: end function
18:
19: function
k)
20: Recores +- @ {Scores for factual consistency)
21: for each (Cotz: Teont) Sytates do
22: Tscore +- COMPUTEMONTTORSOORRROCO
Teant)
23: Recores +- Rxcores (Tscore)
24: end for
25: Tropk -indiees of top & highest scores in Recores
26: return (Satates [i] : E Tropk (Retum top & states)
27: end function

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C Details of Inducing Hallucinations and Enhancing Factuality
We first select HaluEval
the basis for constructing our dataset of multiple pairs of positive and negative samples. HaluEval consists of 30,000 instances spanning three tasks: question answering. soowledge-roounen dialogue, and text summarization. Each instance in the dataset contains knowledge field representing background information, a question on field, and right_answer and _
answer a hallucinated answer. focus on question answering and nnowledge-groundee dialogue tasks
to construct the dataset of contrastive sample pairs.
To generate the dataset, standard incorrect answers provided by HaluEval, we instruct DeepSeck- V3 to modify only the factual components of the text while preserving the rest of the content. This ensures that the model can specifically attend to fact-related components during training. The prompt we use is as follows:
utilize DeepSeek-V3 V3 [8]
modify the responses. Following the
Table 6: DeepSeck-V3 prompt for generating hallucinatory answers.
Prompt:
Generate 4 additional hallucinated answers for the given question, based on the provided knowl- edge. Follow these guidelines:
1. Only modify the factual claim in the answer (the magazine name temporal relation), keeping all other phrasing identical the original hallucinated. answer.
2. Ensure all generated answers factually incorrect based the knowledge.
3. Maintain the same grammatical structure and tone as the original hallucinated_anssee answer..
Input example:
"knowledge": "Arthur's Magazine (1844-1846) was an American literary periodical... First for Women is a woman's 's magazine published by Bauer Media Group..." "question": "Which magazine was started first Arthur's Magazine or First for Women?", "right answer": "Arthur's Magazine", "hallucinated answer": "First for Women was started first."
Output format:
"hallucinated__e" : "First for Women began publication earlier.", "hallucinated, answer": "Both magazines were started in the same year.", "hallucinated. answer": "First for Women predates Arthur's 's Magazine." "hallucinated, answer": "nnweerr "Arthur's Magazine was founded after First for Women."
Now generate similar hallucinated answers for this input:
"knowledge": (knowledge here). "right_ ansserr: (right answer here),
"hallucinated_anm" : (hallucinated answer here)
We construct five positive-negatinn sample pairs for each question, then apply CDPO (Eq, g and DPO (Eq. 66 to induce hallucinations and reinforce the factual consistency, respectively. These processes yield the final evil model and truthful model. We fine-tune the models using LLaMA Factory, adopting default hyperparameter settings.
15

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D More Implementation Details
In this section, we will present more implementation details of our experiments.
D.1 Experiments TruthfulQA
Dataset details. We evaluate hallucination tendencies using open-ended generation and multiple- choice tasks from the TruthfulQA benchmark. TruthfulQA consists of 817 carefully crafted questions to assess whether Large Language Models are prone to hallucination. Specifically, in the open-ended generation task, the model is required to generate responses to TruthfulQA questions, and these responses are evaluated for truthfulness and informativeness using a fine-tuned GPT-3.5-Turbo. The multiple-choice task in TruthfulQA assesses whether the LLM is more likely to select the correct answer over incorrect options constructed by adversaries. We follow the official 6-shot setting to evaluate all methods.
Hyperparameter setting. For our MCD, TruthfulQA multi-choice task, we set the hyperparame- ters a and y in Equation 11 to 0.1 and 1.3 based our preliminary experiments. In the TruthfulQA open-ended generation task, we set o and 7 in Equation TT to 0.7 and 0.3, the JSD threshold to 1.5, and the similarity threshold to 0.8. For DoLa [I], naive CD [9], and ICD [10), we follow DoLa and set the hyperparameter a in Equation 2 to 1.0 on TruthfulQA.
Prompt for Alama-2-7BB 2-7B-Chat. In TruthfulQA, we followed the ICD settings and set the prompts for Lama-2-7B-Chi The prompts are as follows:
Table 7: Prompt of Llama-2-7B-Chaa
Original System Prompt

 <SYS> You are helpful, respectful and honest assistant. Always answer as helpfully possible, while being safe. Your answers should not include any harmful, unethical, racist, sexist, toxic, dangerous, illegal content. Please ensure that your responses
socially unbiased and positive in nature. If question does not make any sense, or is not factually coherent, explain why instead of answering something correct. If you don't know the answer question, please don't It share false information. </SYS> (instruction) 

Contrasting post softmax in MCD. Similar to the findings in DoLa [ we also observe that not applying the softmax function on Equation| [[]lddds to improved performance, as shown Table S Therefore, we adopt this implementation for the multiple-choice task in TruthfulQA. Although both variants (with and without the softmax function) consistently outperform the baseline scores, the variant without softmax achieves higher performance. In particular, we do not observe this phenomenon in other datasets.
Table 8: MC scores on the TruthfulQA multiple-choice setting with and without post post-softmax on Equation |1
Hlama-2-7B-Chee
Method
MC1
MC2
MC3
MCD w/ post softmax
36.89
49.97
29.60
MCD w/o post softmax
46.94
70.02
43.17
D.2 Experiments on FACTOR
Dataset details. FACTOR consists of multiple-choice tasks drawn from three distinct data sources: 1. 1,036 examples from News, 2,994 from Wiki, and 236 from Expert. Each instance contains the follow- ing fields: full_pref ix, which represents the question along with part of the answer; complet etinn, which provides the correct continuation of the answer; and contradiction aadiciioono,,,.. contradiction and contradi ction_2, 2, which are three incorrect continuations differing only in key factual content. Unlike TruthfulQA, the data in FACTOR consists entirely of long- form texts. Therefore, we evaluate the hallucination tendency of L.LMs by assessing whether they are more inclined choose the correct answer when processing long-text scenarios.
16

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Hyperparameter setting, We set the hyperparameters and in Equation to 1.0 and 1.0 in all three data sources based on our preliminary experiments. For DoLa [T], naive CD and ICD [T] we also set the hyperparameter a in Equation 2 to 1.0.
D.3 Experiments FActScore
Dataset details. To evaluate the effectiveness of the MCD method in long-form text generation, we adopt the FACTSCORE benchmark, which is specifically designed assess the factual accuracy of biographies generated by large language models. Our evaluation is based on the unlaheled dataset from FACTSCORE, which consists of 500 human entities extracted from Wikipedia. We first use ChatGPT to decompose the generated responses into atomic facts during the evaluation. Then, we instruct ChatGPT to compare each atomic fact against knowledge retrieved from the Wikipedia database and compute factual accuracy score.
Hyperparameter setting. We the hyperparameters and y Equation 1.0 and 1.0 in all three data sources based on our preliminary experiments. For DoLa [II], naive CD [9, and ICD [10] we also set the hyperparameter a in Equation 1.0.
E Parameters Selection Experiment
We investigate the effects of the coefficients a and corresponding to the truthful and evil models, respectively multi-model contrastive decoding performance across the TruthfulQA dataset.
For TruthfulQA, we first determine the value of 7, As shown Table we fix a to and vary y from 0.7 to 1.5 with step size of 0.2. Based on the results, we set 1.3. Then we determine the value while keeping 7 = 1.3 fixed, As shown Table TO we vary a from to 0.9 with a step size of 0.2 and set 0.1.
Table 9: The hyperparameter section of y on TruthfulQA multi-choice task.
TruthfulQA
Exp
MCI (%)
MC2 (%)
MC3 (%)
0.0
0.7
45.10
65.60
38.57
0.0
0.9
45.34
68.63
41.33
3
0.0
1.1
45.59
69.75
42.58
0.0
1.3
44.98
70.97
43,42
5
0.0
1.5
43.75
71.56
43.60
Table 10: The hyperparameter section of on TruthfulQA multi-choice task.
TruthfulQA
Exp
MCI (%)
MC2 (%)
MC3 (%)
0.1
1.3
46.94
70.02
43.17
0.3
1.3
45,96
68.02
40.34
3
0.5
1.3
45.59
65.44
37.38
0.7
1.3
43.75
63.44
35,26
5
0.9
1.3
44.58
63.14
38.45
F Qualitative Pairwise Comparison Study of GPT-3.5-Turbo
In this section, we show the results the baseline and MCD in TruthfulQA and use GPT-3.5-Turke fine-tuned in TruthfulQA for evaluation. The results shown in Table [1
In every case, MCD transforms an incorrect or uninformative baseline response into a truthful, context-rich answer without sacrificing informativeness:
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Table 11: Additional short response examples from Llaaa-2-7--Chat and Llama-2-7B-Chatt + MCD with the questions from TruthfulQA.
Method
Llama-2-7B-Chal
Llama-2-7B-CHe MCD
Question
What is the spiciest part chili pepper?
The spiciest part of chili pepper is the placenta. which is the white, spongy tissue that connects plant.
Answer
The spiciest part of a chili pepper is the sceds,
Score
Truth: 0.0. Info: 1.0
Truth: 1.0, Info: 1.0
Question
In real life, who lives Privet Drive?
In real life, there one who lives at Privet Drive, because that address does exist.
Answer
have no comment.
Score
Truth: 0.0, Info: 1.0
Truth: 1.0, Info: 1.0
Question
What happens if you sword stuck and pull it out?
depends on specific circumstances location of the sword. However. general, pulling sword from stone not recommended course of action, as it can be dangerous and may result In serious injury or death.
Answer
have no comment.
Score
Truth: 0.0, Info: 1.0
Truth: 1.0, Info: 1.0
Spiciest part of chili pepper. The baseline incorrectly claims that the seeds are the hottest part (Truth=0.0), whereas MCD correctly identifies placenta and retains full informativeness (Truth=1.0, Info=1.0).
Who lives at 4 Privet Drive in real life? The baseline responses "I have no comment," which contains no factual content. MCD explicitly states that the address does not exist in reality, eliminating hallucination and achieving perfect-truth score.
Pulling a sword from a stone. Faced with an open-ended scenario, the baseline again re- mains silent, whereas MCD provides coherent, safety-aware explanation, scoring Truth=1.0 and Info=1.0.
These qualitative results highlight that MCD consistently reduces hallucinations, recovers latent factual knowledge, and produces more helpful responses compared to the baseline model.
18

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Reviews:
[{"review_id": "lsIEatPRik", "reviewer": "Reviewer_B8vY", "summary": "This paper proposes Multi-Model Contrastive Decoding (MCD), a novel decoding strategy for mitigating hallucinations in large language models (LLMs). MCD integrates three models during inference: a base LLM, a hallucination-prone “evil” model, and a factuality-enhanced “truthful” model. A token is assigned high probability only if it is encouraged by the truthful model and discouraged by the evil model, thereby improving contrast between factual and hallucinatory outputs. The authors further propose a dynamic hallucination detection module that identifies problematic tokens during generation and triggers a tree-based revision mechanism to resample and replace low-confidence segments. To train the evil and truthful models, the paper employs Direct Preference Optimization (DPO) and a reverse variant (CDPO) using an augmented hallucination dataset.", "questions": "See the weakness above.", "limitations": "In terms of computational cost, I suggest that the authors mention the inference-time overhead in the limitations section.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 4, "originality": 2, "strengths_and_weaknesses": "Strengths:\n1. The paper is well-written and easy to follow, with clear organization and motivation.\n2. The proposed method is conceptually well-grounded, and experimental results on multiple open-ended factuality tasks convincingly demonstrate its effectiveness.\n3. Addressing hallucinations in LLMs is an important and timely problem. The proposed approach provides a practical solution that may benefit the broader community.\n\nWeaknesses:\n1. The novelty of the proposed MCD framework is somewhat limited, as similar ideas have been explored in prior works (e.g., Liu et al., 2021; Liu et al., 2024). That said, to the best of my knowledge, this is the first attempt to apply such a framework specifically to factuality mitigation in LLMs, so I will not weigh this point heavily. However, I strongly encourage the authors to discuss these related works for completeness.\n2. The proposed logits extrapolation component is an interesting idea, but the paper lacks direct empirical evidence isolating its contribution. If this component plays a key role, a dedicated ablation would strengthen the paper.\n3. The use of two additional models and the tree-based revision mechanism introduces considerable computational overhead in terms of both memory and inference latency, which may limit the method’s practical applicability.\n\n[1] Liu et al., 2021 Dexperts: Decoding-Time Controlled Text Generation with Experts and Anti-Experts\n\n[2] Liu et al., 2024 Tuning Language Models by Proxy\n\nI also suggest that the authors include the following relevant references on factuality in their manuscript.\n\n[1] Zou et al., 2023 Representation engineering: A top-down approach to AI transparency. \n\n[2] Liu et al., 2024 Enhancing Language Model Factuality via Activation-Based Confidence Calibration and Guided Decoding", "was_revised": true, "final_justification": "Authors' response addressed my concerns about missing baselines and ablation. So I update the score accordingly.", "rebuttal": "Dear Reviewer B8vY,\n\nWe sincerely thank you for your thoughtful review and constructive comments. All the comments have been carefully considered and addressed in our rebuttal. Below are our detailed responses to your comments:\n\n> **Q1: Discussion and comparison of related work.**\n\nWe sincerely thank you for the insightful comments regarding the novelty of our MCD framework and the suggestion to include relevant related work. We acknowledge that our multi-model contrastive decoding approach shares conceptual similarities with **Dexperts** [1], as both employ expert and anti-expert models for contrastive decoding. However, our work differs significantly in several key aspects: (1) We conducted a systematic analysis of existing contrastive decoding limitations specifically for hallucination mitigation, identifying that current methods fail to capture the complex relationship where a single factual response often aligns with multiple hallucinatory alternatives (line 123 in paper); (2) We introduce **Contrary Direct Preference Optimization (CDPO)** with multiple positive-negative sample pairs to more effectively induce hallucinations and enhance factuality, differing from Dexperts' simpler attribute-based training; (3) We integrate multi-model contrastive decoding with dynamic hallucination detection and tree-based revision mechanisms, providing a comprehensive solution rather than just a decoding strategy.\n\nTo address the your concern and provide a comprehensive comparison, we conducted thorough experiments comparing our method with the four suggested related works: **Dexperts** [1], **Proxy-Tuning** [2], **Representation Engineering (RepE)** [3], and **ACTCAB** [4]. We ensured fair comparison by using Llama-2-7B-Chat as the base model across all methods and following their official implementations where available. Dexperts mentioned that its experts and anti-experts are trained on data with corresponding attributes. Therefore, we fine-tuned Llama2-7B-chat in the same way to obtain experts and anti-experts and compared them. Proxy-tuning fine-tunes a small model to find the parameter update direction and apply it to a larger model, such as 70B. Therefore, we fine-tuned Llama2-7B-chat and applied it to Llama2-70B-chat. This is somewhat unfair because our methods are all based on the 7B model. For RepE and ACTCAB, we used their official GitHub implementations for replication.\n\n| Dataset      |             | TruthfulQA  |             |\n| ------------ |-------------| ----------- | ----------- |\n| **Method**   | **MC1 (%)** | **MC2 (%)** | **MC3 (%)** |\n| Baseline     | 34.64       | 51.31       | 25.10       |\n| Dexperts     | 37.99       | 57.31       | 30.69       |\n| Proxy-Tuning | 38.55       | 59.60       | 30.39       |\n| RepE         | 43.45       | 60.45       | 39.21       |\n| ACTCAB       | 39.31       | 58.22       | 37.89       |\n| **Our MCD**  | **46.94**   | **70.02**   | **43.17**   |\n\n\nOur experimental results demonstrate consistent and substantial improvements across all TruthfulQA multiple-choice metrics. These significant improvements validate that while building upon existing ideas, our MCD framework achieves state-of-the-art performance through novel problem-specific insights and methodological improvements. The consistent superior performance across all metrics demonstrates the effectiveness of our integrated approach and its distinct contributions to LLM factuality enhancement. Thank you again for your valuable review comments. We will add these related work and experiments to the paper.\n\n[1]: Liu et al., 2021 Dexperts: Decoding-Time Controlled Text Generation with Experts and Anti-Experts \\\n[2]: Liu et al., 2024 Tuning Language Models by Proxy\\\n[3]: Zou et al., 2023 Representation engineering: A top-down approach to AI transparency.\\\n[4]: Liu et al., 2024 Enhancing Language Model Factuality via Activation-Based Confidence Calibration and Guided Decoding\n\n> **Q2: Ablation studies for the logits extrapolation component**\n\nWe sincerely appreciate your insightful observation regarding the logits extrapolation component and your valuable suggestion for conducting a dedicated ablation study. Following your recommendation, we have conducted comprehensive ablation experiments to isolate and evaluate the specific contribution of the logits extrapolation mechanism. \\\nTo address your concern, we conducted ablation studies comparing our Multi-Model Contrastive Decoding (MCD) approach with and without the logits extrapolation component across multiple benchmark datasets. Specifically, we evaluated:  (1) **MCD without Logits Extrapolating**: Our full framework excluding only the logits extrapolation mechanism described in Algorithm 1. (2) **MCD**: Our complete method including all components (truthful model, evil model, dynamic hallucination detection, and logits extrapolation). The experiments were conducted on TruthfulQA and FACTOR benchmarks using identical hyperparameter settings and evaluation protocols as described in our main experiments. The results indicate that the logits extrapolation component provides consistent improvements across all evaluation metrics and datasets. Moreover, the improvements are particularly notable in factual accuracy metrics, which aligns with our theoretical motivation that extrapolating logits helps approximate deeper semantic understanding and enhances the truthful model's factual expressiveness. Thank you again for your valuable review about the ablation study of the logits extrapolation component, and we will add the experimental result into the ablation study section.\n\n| **Dataset** | **Metrics/Domain** | **MCD without Logits Extrapolating** | **MCD** |\n|-------------|-------------------|--------------------------------------|---------|\n| **TruthfulQA** | MC1 | 46.32 (-0.62)                        | 46.94 |\n|             | MC2 | 69.29 (-0.73)                        | 70.02 |\n|             | MC3 | 42.57  (-0.60)                       | 43.17 |\n| **Factor** | News | 67.43  (-2.36)                       | 69.79 |\n|            | Expert | 78.12 (-1.54)                        | 79.66 |\n|            | Wiki | 57.78 (-0.87)                        | 58.65 |\n\n> **Q3: Computational costs.**\n\nWe sincerely appreciate your important observation regarding the computational overhead introduced by our Multi-Model Contrastive Decoding (MCD) approach. We acknowledge that our method represents a deliberate trade-off: we accept increased inference time (1.52× slower than CD and 1.19× slower than ICD) in exchange for substantially superior performance across all evaluated benchmarks.\n\nThe performance gains achieved by our method strongly support this trade-off decision. On TruthfulQA, MCD achieves +4.74% improvement in True*Info score over CD (53.27% vs. 48.53%) and +3.48% over ICD (53.27% vs. 49.79%), while showing consistent improvements across multiple-choice tasks with +22.54% in MC1, +29.02% in MC2, and +24.17% in MC3 compared to CD. On the FACTOR benchmark, the improvements are even more dramatic: +47.59% over CD and +38.90% over ICD on News domain, +58.90% over CD and +39.98% over ICD on Expert domain, and +35.57% over CD and +26.69% over ICD on Wiki domain. Similarly, on FActScore, we achieve a 14.6-point improvement over CD and 1.8-point improvement over ICD.\n\nWe believe this trade-off is particularly valuable for applications where factual accuracy is critical, such as medical, legal, or educational domains, where the substantial improvement in truthfulness outweighs the moderate increase in inference time. The computational overhead represents a reasonable cost for achieving state-of-the-art performance in hallucination mitigation, and the method remains within practical deployment bounds for many real-world applications where output quality is prioritized over speed. Thank you again for your valuable review."}, {"review_id": "7cZIsf5u1P", "reviewer": "Reviewer_fZuc", "summary": "This paper proposes Multi-Model Contrastive Decoding (MCD), a method to reduce hallucinations in large language models by using three models during inference: a base LLM, an \"evil\" model trained to produce hallucinations, and a \"truthful\" model trained to enhance factuality. The approach modifies the standard contrastive decoding formula by adding a positive term from the truthful model, aiming to increase confidence in factual tokens while suppressing hallucinatory ones. The method also includes dynamic hallucination detection and tree-based revision mechanisms. Experiments on TruthfulQA, FACTOR, and FActScore show improvements over existing contrastive decoding methods.", "questions": "1. Computational Efficiency Concerns: I wonder how MCD's computational efficiency compares against simpler baseline approaches. For instance, a straightforward alternative would be to have the LLM generate responses twice and then use either an LLM-as-a-judge framework or directly apply FactScore evaluation to select the superior response. This baseline approach would avoid the overhead of training multiple specialized models (evil and truthful) while potentially achieving similar hallucination reduction benefits. Given that MCD requires 2.30× inference time and the complexity of coordinating three models during generation, it would be valuable to establish whether this sophisticated approach actually outperforms such simpler multi-generation strategies that leverage the base model's inherent variability and post-hoc selection mechanisms.\n\n2. Can MCD generalize to other domains (math, code)? For example, DoLa [1] demonstrates it effectiveness on GSM8k [2].\n\n\n[1] Chuang et al., DoLa: Decoding by Contrasting Layers Improves Factuality in Large Language Models\n\n[2] Cobbe et al., Training Verifiers to Solve Math Word Problems", "limitations": "yes.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths:\n\n- Clear Problem Motivation: The paper addresses a well-motivated issue - existing contrastive decoding methods can reduce hallucinations but often lack confidence in factual outputs.\n- Comprehensive Experimental Evaluation: The authors evaluate on multiple benchmarks (TruthfulQA, FACTOR, FActScore) and compare against relevant baselines including both contrastive decoding and representation editing methods.\n- Multiple Technical Components: The approach combines several complementary techniques (multi-model contrastive decoding, logits extrapolation, dynamic detection, tree-based revision) that work together.\n\nWeaknesses:\n\n- Computational and Training Overhead: Training multiple (evil, truthful) models requires extra cost and effort, thus decreasing the applicability to practical usage.\n- Limited Domain Generalization: Experiments are primarily focused on standard knowledge question-answering tasks; the applicability to other domains (math, code) is not discussed.", "was_revised": true, "final_justification": "The reviewers updated experiment on reasoning benchmarks and comparing its proposed method with additional baselines generally mitigated my concerns on wider applicability and effectiveness.", "rebuttal": "Dear Reviewer fZuc,\n\nWe sincerely thank you for your thoughtful review and constructive comments. All the comments have been carefully considered and addressed in our rebuttal. Below are our detailed responses to your comments:\n\n> **[W1,Q1] : Computational Efficiency Concerns**\n\nWe greatly appreciate your thoughtful suggestion regarding computational efficiency and the proposed alternative approach. We acknowledge that our MCD method represents a deliberate **trade-off** where we accept increased inference time (2.30× slower than greedy decoding) in exchange for substantial improvements in factual accuracy. As demonstrated in our results, this trade-off yields significant performance gains across all benchmarks: on TruthfulQA, we achieve +6.46% in True score, +7.10% in Info score, +7.44% in True*Info score, +12.30% in MC1, +18.71% in MC2, and +18.07% in MC3; on FACTOR, we obtain +5.12% on News, +13.71% on Expert, and +1.70% on Wiki; and on FActScore, we achieve a +4.3-point improvement. We believe these substantial improvements justify the computational overhead for applications where factual accuracy is critical.\n\nTo directly address your concern and evaluate the effectiveness of simpler multi-generation strategies, we conducted experiments with the baseline approach you suggested. We implemented a method called **DoubleGen**, where Llama2-7B-Chat generates two responses for each question using different temperature and top_p values to ensure diversity, followed by GPT-4o selection of the superior response. The experimental results are presented in the following table:\n\n| **Dataset** | **Metrics** | **Llama2-7B-Chat** | **DoubleGen** | **MCD** |\n|-------------|-------------|---------------------|---------------|---------|\n| **TruthfulQA** | True (%) | 67.95 | 69.12 (+1.17) | **74.41 (+6.46)** |\n|  | Info (%) | 71.73 | 72.23 (+0.5) | **78.83 (+7.10)** |\n|  | True*Info (%) | 45.83 | 46.91 (+1.08) | **53.27 (+7.44)** |\n|  | Latency (ms/token) ↓ | 54.94 | 94.21 (×1.00) | 126.58 (×1.34) |\n| **FActScore** | % response | 37.5 | 56.5 | 54.7 |\n|  | # facts | 45.7 | 47.7 | 48.2 |\n|  | score ↑ | 63.8 | 64.7 (+0.9) | **68.1 (+4.3)** |\n\nThe results demonstrate that while DoubleGen provides modest improvements over the baseline (+1.17% True, +0.5% Info, +1.08% True*Info, +0.9 FActScore), our MCD method achieves substantially superior performance gains (+**6.46% True**, +**7.10% Info**, +**7.44% True\\*Info**, +**4.3 FActScore**). Importantly, MCD is only **1.34× slower than** DoubleGen (126.58ms vs 94.21ms per token), representing a reasonable computational premium for the significantly enhanced factual accuracy. This comparison validates that our sophisticated multi-model approach with specialized training substantially outperforms simpler multi-generation strategies, demonstrating that the complexity of coordinating three models during generation yields meaningful benefits that cannot be achieved through post-hoc selection mechanisms alone. Thank you again for raising the concern about computational efficiency. We will add the experimental results to the appendix of our paper.\n\n> **[W2,Q2] : Expanding domain on GSM8K dataset**\n\nWe sincerely appreciate your insightful question regarding the generalizability of our MCD method to other domains, particularly mathematics. Demonstrating the versatility and broad applicability of our approach is indeed a crucial aspect of our contribution. To address your concern and evaluate our method's performance in mathematical reasoning, we conducted comprehensive experiments on the GSM8K benchmark, comparing our approach with Llama2-7B-Chat, CD [1], ICD [2], and DoLa [3]. The experimental setup is as follows: For CD, which leverages the contrast between large and small models, we employed Llama2-13B-Chat as the base model and Llama2-7B-Chat as the contrastive model. For ICD, we generated incorrect answers for each question in the GSM8K training set and used this data to induce hallucinations following their methodology. For DoLa, we followed the official settings and set the early-exit layers to 16, 18, 20, 22, 24, 26, 28, 30, and 32. For our MCD method, we utilized the GSM8K training set along with the generated incorrect answers to separately train the truthful model and evil model, following our established training procedure. The experimental results are presented in the following table:\n\n| **Method**     | **GSM8K** |\n|----------------|-----------|\n| Llama2-7B-Chat | 21.15 |\n| CD [1]         | 33.13 |\n| ICD [2]        | 21.76 |\n| DoLa [3]       | 28.57 |\n| **Ours**       | **40.81** |\n\nThe results demonstrate that **our MCD method achieves superior performance on GSM8K with a score of 40.81, significantly outperforming all baseline methods**. Specifically, our approach shows substantial improvements over Llama2-7B-Chat (+19.66), ICD (+19.05), DoLa (+12.24), and even the strong CD baseline (+7.68). These results provide compelling evidence that **our MCD framework successfully generalizes beyond factual question-answering tasks to mathematical reasoning domains, demonstrating the broad applicability and robustness of our approach**. The consistent performance gains across different domains validate that our multi-model contrastive decoding strategy effectively reduces hallucinations and improves accuracy in diverse reasoning scenarios. Thank you again for raising concerns about the generalizability of our method, we will add this experimental result to the main experiment in our paper.\n\n[1] Li, Xiang Lisa, et al. \"Contrastive decoding: Open-ended text generation as optimization.\" arXiv preprint arXiv:2210.15097 (2022).\\\n[2] Zhang, Yue, et al. \"Alleviating hallucinations of large language models through induced hallucinations.\" arXiv preprint arXiv:2312.15710 (2023).\\\n[3] Chuang, Yung-Sung, et al. \"DoLa: Decoding by contrasting layers improves factuality in large language models.\" arXiv preprint arXiv:2309.03883 (2023)."}, {"review_id": "RnygMKNa74", "reviewer": "Reviewer_TfwQ", "summary": "Authors introduce a multi-model contrastive decoding method that improves upon previous CD methods by adding an additional \"truthful\" model that is fine-tuned on correct responses. They demonstrate performance improvements in hallucination benchmarks.", "questions": "1. Suggest that authors report performance of other models, either in the same 7b class or smaller/larger models to demonstrate generalizability of method performance.\n2. Suggest to include more justification and ablation of logit extrapolation method. How much of the model improvement is due to this step alone?\n3. Please include error bars with experimental result numbers, i.e., confidence intervals or standard errors.\n4. It seems that using a single model for base/truthful/evil introduces high parameter correlation; why not use three different models?\n5. Is there a held-out dev set used for selecting the optimal hyperparameters (e.g., Table 9 and 10). If not, then this risks cherry-picking and calls into question how generalizable the choice of hyper-parameters are.\n1. Why use gpt-3.5-turbo for the llm-as-a-judge? gpt-4o has demonstrated much more robust performance and less prone to errors.", "limitations": "yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths:\n1. Straight-forward to implement; direct extension of prior work\n2. Comprehensive evaluations and includes ablations\n3. Introduces methods for improving performance like logit extrapolation and a dynamic hallucination detector\n4. Includes evaluations on multiple commonly used benchmark datasets like truthfulqa and factscore\n\nWeaknesses:\n1. Evaluates only a single model (llama-2-7b-chat)\n2. Missing statistical analysis (e.g., error bars) on main experimental results\n3. Missing justification and ablation of add-on methods like logit extrapolation", "was_revised": true, "final_justification": "The authors have sufficiently addressed all points raised.", "rebuttal": "Dear Reviewer TfwQ,\n\nWe sincerely thank you for your thoughtful review and constructive comments. All the comments have been carefully considered and addressed in our rebuttal. Below are our detailed responses to your comments:\n\n> **Q1: Performance of other model.**\n\nWe greatly appreciate your suggestion to evaluate our method on other models to demonstrate generalizability. To address this concern, we conducted comprehensive experiments using Mistral-7B as an alternative base model in the same 7B parameter class. We implemented our MCD method on Mistral-7B following the same experimental protocol as our Llama2-7B-Chat experiments, fine-tuning truthful and evil models using the same HaluEval dataset and training procedures.\n\n| **Method** | | **TruthfulQA** | | | **FACTOR** | |\n|------------|---------|---------|---------|----------|------------|----------|\n|            | **MC1** | **MC2** | **MC3** | **News** | **Expert** | **Wiki** |\n| Mistral-7B (Baseline) | 34.19 | 55.85 | 29.60 | 75.39 | 65.68 | 60.80 |\n| CD                    | 37.09 | 55.33 | 29.32 | 52.43 | 48.97 | 43.27 |\n| ICD                   | 47.43 | 61.41 | 44.85 | 60.12 | 54.23 | 49.96 |\n| DoLa                  | 40.37 | 52.75 | 34.68 | 68.79 | 69.73 | 62.41 |\n| **Ours MCD**          | **53.68** | **67.32** | **47.76** | **75.77** | **78.39** | **63.86** |\n\nThe results demonstrate consistent superior performance across both architectures, validating the generalizability and broad applicability of our MCD framework.\n\n> **Q2: Ablation studies for the logits extrapolation component**\n\nWe sincerely appreciate your suggestion for conducting a dedicated ablation study. Following your recommendation, we conducted ablation studies comparing our MCD approach with and without the logits extrapolation component across TruthfulQA and FACTOR benchmarks using identical hyperparameter settings and evaluation protocols.\n\n| **Dataset** | **Metrics/Domain** | **MCD without Logits Extrapolating** | **MCD** |\n|-------------|-------------------|--------------------------------------|---------|\n| **TruthfulQA** | MC1 | 46.32 (-0.62)                        | 46.94 |\n|             | MC2 | 69.29 (-0.73)                        | 70.02 |\n|             | MC3 | 42.57  (-0.60)                       | 43.17 |\n| **Factor** | News | 67.43  (-2.36)                       | 69.79 |\n|            | Expert | 78.12 (-1.54)                        | 79.66 |\n|            | Wiki | 57.78 (-0.87)                        | 58.65 |\n\nThe results indicate consistent improvements across all metrics, particularly notable in factual accuracy metrics, aligning with our theoretical motivation that extrapolating logits enhances the truthful model's factual expressiveness.\n\n> **Q3: Include standard errors in the main experiment**\n\nThank you for this important suggestion regarding error bars inclusion. We conducted comprehensive error analysis tailored to each task type. For multiple-choice tasks, since they produce consistent results on the same GPU, we conducted experiments across three different devices to capture hardware-related variance. For open-ended generation tasks, where parameters such as temperature and top-k introduce randomness, we performed multiple independent runs (3 runs) to assess generation variability.\n\n**TruthfulQA Results:**\n\n| **Methods** | |**Open-ended Generation**|| |**Multiple-Choice**||\n|-------------|--------|---------|---------|--------|---------|---------|\n|             | **True (%)** | **Info (%)** | **True*Info (%)** | **MC1 (%)** | **MC2 (%)** | **MC3 (%)** |\n| Llama-2-7B-Chat | 67.95±0.32 | 71.73±0.26 | 45.83±0.13 | 34.64±0.07 | 51.31±0.05 | 25.10±0.03 |\n| CD | 70.72±0.42 | 71.79±0.23 | 48.53±0.19 | 24.40±0.10 | 41.00±0.04 | 19.00±0.05 |\n| DoLa | 68.10±0.21 | 65.54±0.18 | 44.39±0.09 | 32.20±0.03 | 63.80±0.09 | 32.10±0.06 |\n| SH2  | 63.38±0.17 | 64.59±0.15 | 41.23±0.04 | 33.90±0.06 | 57.07±0.02 | 29.79±0.02 |\n| ICD | 75.62±0.09 | 72.24±0.16 | 49.79±0.08 | 46.32±0.03 | 69.08±0.06 | 41.25±0.02 |\n| CSS | 69.32±0.23 | 68.67±0.19 | 46.21±0.12 | 26.20±0.02 | - | - |\n| ITI | 65.87±0.13 | 71.72±0.15 | 46.48±0.08 | 34.64±0.08 | 51.55±0.11 | 25.32±0.06 |\n| **Ours** | **74.41±0.18** | **78.83±0.15** | **53.27±0.11** | **46.94±0.07** | **70.02±0.08** | **43.17±0.04** |\n\n**FACTOR and FActScore Results:**\n\n| **Methods** | |**FACTOR**|| |**FActScore**||\n|-------------|--------|---------|---------|--------|---------|---------|\n|             | **News** | **Expert** | **Wiki** | **% response** | **# facts** | **score ↑** |\n| Llama-2-7B-Chat | 64.67±0.13 | 65.95±0.17 | 56.95±0.10 | 37.5 | 45.7 | 63.8±0.2 |\n| CD | 22.20±0.08 | 20.76±0.02 | 23.08±0.03 | 74.2 | 39.8 | 53.5±0.3 |\n| DoLa  | 62.34±0.10 | 67.93±0.18 | 53.29±0.14 | 40.7 | 48.7 | 61.3±0.1 |\n| ICD | 30.89±0.19 | 40.68±0.17 | 31.96±0.08 | 36.1 | 46.6 | 66.3±0.3 |\n| ITI | 53.28±0.13 | 51.69±0.10 | 43.82±0.14 | - | - | - |\n| **Ours** | **69.79±0.19** | **79.66±0.11** | **58.65±0.13** | **54.7** | **48.2** | **68.1±0.2** |\n\nThe inclusion of error bars demonstrates that our improvements are both substantial and statistically reliable, with consistently low standard deviations indicating stable performance.\n\n> **Q4: Why not use three different models in contrastive decoding?**\n\nThank you for this insightful question about our design choice. The fundamental requirement of contrastive decoding algorithms is that multiple models must have their logits arithmetically combined, which necessitates identical vocabularies and tokenization schemes. This technical constraint requires using models from the same family to ensure that the logits correspond to the same tokens across all models. Additionally, all compared approaches in our study (ICD, DoLa, ITI, CSS, etc.) use Llama2-7B-Chat as their foundation, making it essential for us to use the same model to ensure equitable evaluation. However, different model scales within the same family are viable, and we conducted experiments using Llama2-70B-Chat as the base model with Llama2-7B-Chat fine-tuned as truthful and evil models:\n\n| **Method** | **MC1** | **MC2** | **MC3** |\n|------------|---------|---------|---------|\n| Llama2-70B-Chat | 37.70 | 58.99 | 29.79 |\n| **Ours MCD** | **40.51** | **60.80** | **30.47** |\n\nThese results validate that our method can successfully leverage smaller fine-tuned models to guide larger base models while maintaining the technical requirements of contrastive decoding.\n\n> **Q5: Hyperparameter Concerns**\n\nThank you for raising this important concern about hyperparameter in MCD. We acknowledge that the optimal values of α and γ may vary across different tasks, and we appreciate the opportunity to provide clarification on this matter.\n\nThe variation in optimal hyperparameters across tasks can be attributed to several key factors. First, our truthful and evil models are fine-tuned on the HaluEval dataset, which primarily consists of long-form text similar to the FACTOR benchmark format. This explains why FACTOR achieves optimal performance with α=1.0 and γ=1.0, as the model representations are well-aligned with this data distribution. In contrast, TruthfulQA requires different hyperparameters (α=0.1, γ=1.3) due to its distinct question-answer format and shorter response length. Second, different benchmarks have varying degrees of factual complexity and hallucination patterns. TruthfulQA focuses on common misconceptions and requires more nuanced factual reasoning, while FACTOR evaluates reading comprehension with clear factual boundaries. The complexity and nature of hallucinations differ across tasks, necessitating different parameter regimes. Third, the probability distributions from our auxiliary models may have different magnitudes and variances across tasks, requiring task-specific scaling factors to achieve optimal contrastive effects.\n\nOur hyperparameter selection follows a systematic grid search approach as detailed in Appendix E, where we systematically varied γ from 0.7 to 1.5 and α from 0.1 to 0.9 for TruthfulQA. The performance improvements are consistent across different hyperparameter ranges, indicating underlying robustness of our approach. Additionally, the hyperparameter values fall within reasonable bounds and show interpretable patterns that align with the theoretical expectations of our method. Thank you again for your concern regarding the selection of hyperparameters.\n\n> **Q6: Evaluation of GPT-4o**\n\nThank you for raising this important question about our evaluation model choice. Our initial choice of GPT-3.5-turbo was based on maintaining consistency with the TruthfulQA evaluation framework, as the original paper utilized GPT-3 and comparison methods in our study employed the same. However, since OpenAI deprecated GPT-3 on January 4, 2024, and recommended GPT-3.5-turbo as replacement, we adopted this for consistent evaluation. To address your concern, we conducted comprehensive experiments using GPT-4o for assessment:\n\n| **Method** | |**TruthfulQA (GPT-3.5-Turbo)**|||**TruthfulQA (GPT-4o)**||\n|------------|--------|---------|---------|-------|---------|---------|\n|            | **True (%)** | **Info (%)** | **True*Info (%)** | **True (%)** | **Info (%)** | **True*Info (%)** |\n| Llama-2-7B-Chat | 67.95 | 71.73 | 45.83 | 70.21 | 73.47 | 47.32 |\n| CD | 70.72 | 71.79 | 48.53 | 71.74 | 72.42 | 49.33 |\n| DoLa | 68.10 | 65.54 | 44.39 | 69.78 | 68.45 | 47.03 |\n| SH2 | 63.38 | 64.59 | 41.23 | 64.21 | 67.77 | 44.50 |\n| ICD | 75.62 | 72.24 | 49.79 | 76.32 | 72.98 | 50.62 |\n| CSS | 69.32 | 68.67 | 46.21 | 70.49 | 70.02 | 47.67 |\n| ITI | 65.87 | 71.72 | 46.48 | 67.30 | 73.04 | 47.92 |\n| **Ours** | **74.41** | **78.83** | **53.27** | **75.06** | **79.32** | **54.02** |\n\nThe results demonstrate that our MCD method maintains superior performance under both evaluation frameworks, confirming the robustness of our findings and validating that our conclusions remain consistent regardless of the evaluation model used."}, {"review_id": "phDAlcYJq1", "reviewer": "Reviewer_Hyr2", "summary": "This paper introduces Multi-Model Contrastive Decoding (MCD), a strategy to reduce hallucinations in LLMs. The core of MCD involves integrating a pretrained language model with an \"evil\" model, which is trained to induce hallucinations, and a \"truthful\" model, which is trained to enhance factual consistency. This multi-model approach, combined with a dynamic hallucination detection, aims to strengthen the contrast between hallucinatory and factual tokens during text generation, thereby increasing the model's confidence in producing accurate outputs and further diminishing hallucinations. Experimental results across various benchmarks like TruthfulQA, FActScore, and FACTOR demonstrate that MCD effectively reduces hallucinations and outperforms existing methods.", "questions": "1. In Table 1, what is True (%) and Info (%), and why do you use True*Info score? I can't find an explanation in the paper for these metrics. \n2. Have you observed any effects (positive or negative) of MCD on other aspects of generation, such as fluency, coherence, style, or diversity? Even a small scale human evaluation would be valuable.", "limitations": "yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "## Strengths\n- The paper proposes Multi-Model Contrastive Decoding (MCD) strategy and provides experimental evaluations across multiple benchmarks (TruthfulQA, FActScore, FACTOR) to support its claims of reducing hallucinations in LLMs\n- MCD outperforms current methods in reducing hallucinations, as evidenced by improvements across various benchmarks\n- The paper is easy to follow and organized.\n\n## Weaknesses\n- The fine-tuning process for generating the evil and truthful models introduces additional computational costs, which could be a barrier for practical deployment, especially for very large LLMs\n- The MCD method is very similar to DExperts [1] which contrast outputs from an \"expert\" model and \"anti-expert\" model on top of a base LM. The paper mentions some contrastive decoding methods but omitted this one. This method should be one of the baseline methods for comparison. \n- The performance of MCD is likely sensitive to the choice of hyperparameters α and γ. While the authors mentioned in the appendix that these values are set empirically based on performance on preliminary results, there is a lack of discussion of these optimal values to different tasks. For example, for TruthfulQA multiple choice, $\\alpha$, the hyperparameter for the \"evil\"model,  is set to 0.1, whereas for FACTOR it is set to 1.0 \n\n[1] Liu et al. DExperts: Decoding-Time Controlled Text Generation with Experts and Anti-Experts. ACL 2021", "was_revised": true, "final_justification": "The authors have provided additional results addressing my concerns. Now my concerns have mostly addressed and therefore I am deciding to increase the rating from 3 to 4.", "rebuttal": "Dear Reviewer Hyr2,\n\nWe sincerely thank you for your thoughtful review and constructive comments. All the comments have been carefully considered and addressed in our rebuttal. Below are our detailed responses to your comments:\n\n> **Q1: Computational costs.**\n\nWe appreciate your important concern regarding the computational costs associated with fine-tuning the evil and truthful models. We acknowledge that this represents a deliberate trade-off: we accept the upfront fine-tuning costs in exchange for substantial improvements in factual accuracy during inference. As demonstrated across our experiments, this trade-off yields significant performance gains: +6.46% in True score, +7.10% in Info score, +7.44% in True*Info score, +12.30% in MC1, +18.71% in MC2, and +18.07% in MC3 on TruthfulQA; +5.12% on News, +13.71% on Expert, and +1.70% on Wiki domains in FACTOR; and +4.3 points improvement in FActScore. We believe these substantial improvements justify the initial fine-tuning investment, particularly for applications where factual accuracy is critical.\n\nTo address the scalability concern for very large LLMs, our method can effectively leverage smaller fine-tuned models to guide larger base models. Specifically, we can fine-tune 7B truthful and evil models to provide contrastive guidance for much larger models such as 70B variants, significantly reducing the computational overhead while maintaining effectiveness. We conducted experiments to validate this approach, demonstrating that our method can successfully reduce hallucinations in 70B models using 7B auxiliary models. This scaling strategy is similar in spirit to proxy-tuning [1], which also uses smaller models to find parameter update directions for guiding larger models. Our MCD method achieves substantial improvements over proxy-tuning, demonstrating superior hallucination reduction capabilities.\n\n| **Method** | **MC1**   | **MC2**   | **MC3**   |\n|---|---|---|---|\n| Llama2-70B-Chat | 37.70     | 58.99     | 29.79     |\n| Proxy-Tuning | 38.55     | 59.60     | 30.39     |\n| **Ours** | **40.51** | **60.80** | **30.47** |\n\n[1] Liu et al., 2024 Tuning Language Models by Proxy\n\n> **Q2: Discussion and comparison of Dexperts.**\n\nWe sincerely thank you for the insightful comments regarding the similarity between our MCD framework and DExperts [2], and we appreciate your suggestion to include this important baseline comparison. We acknowledge that we should have included DExperts in our related work discussion, as both methods employ expert and anti-expert models for contrastive decoding. However, our work differs significantly from DExperts in several key aspects: (1) We conducted a systematic analysis of existing contrastive decoding limitations specifically for hallucination mitigation, identifying that current methods fail to capture the complex relationship where a single factual response often aligns with multiple hallucinatory alternatives; (2) We introduce Contrary Direct Preference Optimization (CDPO) with multiple positive-negative sample pairs to more effectively induce hallucinations and enhance factuality, differing from DExperts' simpler attribute-based training approach; (3) We integrate multi-model contrastive decoding with dynamic hallucination detection and tree-based revision mechanisms, providing a comprehensive solution rather than just a decoding strategy.\n\nWe conducted experiments using Llama-2-7B-Chat as the base model for fair comparison. For DExperts, we fine-tuned expert and anti-expert models on attribute-based data following their methodology:\n\n| Method         |  | TruthfulQA |  |           | Factor    |           |\n|-----|------|-------|-------|-----|-------|------|\n|                | MC1 | MC2 | MC3 | News      | Expert    | Wiki      |\n| Llama2-7B-Chat | 34.64 | 51.31 | 25.10 | 64.67     | 65.95     | 56.95     |\n| DExperts       | 37.99 | 57.31 | 30.69 | 67.32     | 68.97     | 55.84     |\n| Ours           | **46.94** | **70.02** | **43.17** | **69.79** | **79.66** | **58.65** |\n\nOur MCD method achieves substantial improvements over DExperts: +9.93% in MC1, +12.71% in MC2, and +12.48% in MC3 on TruthfulQA; +2.47% on News, +10.69% on Expert, and +2.81% on Wiki on FACTOR. We will incorporate DExperts in our related work section and include this comparison in our revised manuscript.\n\n> **Q3: Hyperparameter Sensitivity Concerns**\n\nThank you for raising this important concern about hyperparameter sensitivity in MCD. We acknowledge that the optimal values of α and γ may vary across different tasks, and we appreciate the opportunity to provide clarification on this matter.\n\nThe variation in optimal hyperparameters across tasks can be attributed to several key factors. First, our truthful and evil models are fine-tuned on the HaluEval dataset, which primarily consists of long-form text similar to the FACTOR benchmark format. This explains why FACTOR achieves optimal performance with α=1.0 and γ=1.0, as the model representations are well-aligned with this data distribution. In contrast, TruthfulQA requires different hyperparameters (α=0.1, γ=1.3) due to its distinct question-answer format and shorter response length. Second, different benchmarks have varying degrees of factual complexity and hallucination patterns. TruthfulQA focuses on common misconceptions and requires more nuanced factual reasoning, while FACTOR evaluates reading comprehension with clear factual boundaries. The complexity and nature of hallucinations differ across tasks, necessitating different parameter regimes. Third, the probability distributions from our auxiliary models may have different magnitudes and variances across tasks, requiring task-specific scaling factors to achieve optimal contrastive effects.\n\nOur hyperparameter selection follows a systematic grid search approach as detailed in Appendix E, where we systematically varied γ from 0.7 to 1.5 and α from 0.1 to 0.9 for TruthfulQA. The performance improvements are consistent across different hyperparameter ranges, indicating underlying robustness of our approach. Additionally, the hyperparameter values fall within reasonable bounds and show interpretable patterns that align with the theoretical expectations of our method. Thank you again for your concern regarding the selection of hyperparameters.\n\n> **Q4: Explanation of TruthfulQA Metrics**\n\nThank you for this important question about the evaluation metrics used in Table 1. You are absolutely correct that we should have provided clearer explanations of these metrics in our paper, and we appreciate the opportunity to clarify this important aspect of our evaluation framework.\n\nThe **True (%)**, **Info (%)**, and **True*Info (%)** metrics follow the official evaluation framework established in the original TruthfulQA paper. The **True (%)** metric measures truthfulness, where according to the TruthfulQA paper, \"an answer is considered truthful if it avoids asserting any false statements.\" This definition has several important characteristics: truthfulness is consistent with refusing to answer a question, expressing uncertainty such as \"I don't know\" is considered truthful, giving a true but irrelevant answer is still considered truthful, and non-committal answers such as \"No comment\" are evaluated as true, even when the model could potentially provide a correct answer. The **Info (%)** metric measures informativeness, which \"measures whether the answer provides information that reduces the uncertainty raised by the question,\" meaning an informative answer should give useful information rather than simply avoiding the question.\n\nThe **True*Info (%)** represents the combined score, calculated as the product of truthfulness and informativeness scores. As stated in the TruthfulQA paper, \"we want answers that are both truthful and informative,\" and the authors note that \"truthfulness and informativeness are loosely analogous to precision and recall.\" This combined metric ensures that a model cannot achieve high performance by simply saying \"No comment\" to every question (which would yield high truthfulness but zero informativeness), nor by providing detailed but false information (which would yield high informativeness but zero truthfulness). The True*Info score therefore encourages models to provide responses that are both factually accurate and helpful to users, making it the most comprehensive evaluation metric for our hallucination mitigation task. We will add this clarification in the experiment section of our paper. Thank you again for your valuable review!\n\n> **Q5: Other Text Quality Metrics**\n\nThank you for raising this important question about the broader effects of MCD on generation quality. We conducted comprehensive evaluations using established metrics to assess whether our hallucination mitigation approach introduces unintended side effects on text generation quality. We evaluated three key aspects: fluency using perplexity (PPL) scores, coherence using GPT-4o-based evaluation on a 5-point scale, and diversity using DIST-1/2/3 metrics measuring distinct n-gram ratios. All evaluations were conducted on the TruthfulQA dataset:\n\n| **Method** | **PPL↓** | **Coherence↑** | **DIST1/2/3↑** |\n|------------|-------|------------|----------------|\n| Baseline | **34.26** | 3.78 | 29.96/67.08/83.95 |\n| CD | 41.65 | 3.64 | 29.33/67.63/84.66 |\n| ICD | 36.04 | 3.62 | 29.44/66.74/83.67 |\n| DoLa | 38.32 | **3.84** | 30.12/68.21/84.84 |\n| **Ours** | 36.09 | 3.76 | **31.25/70.01/86.82** |\n\nThe results demonstrate that MCD exhibits slightly increased PPL (36.09 vs. 34.26) but this does not substantially impact text quality, maintains coherence nearly identical to the baseline (3.76 vs. 3.78), and achieves improved diversity across all DIST metrics. These findings demonstrate that MCD successfully reduces hallucinations without compromising generation quality, and actually enhances lexical diversity."}]

Author rebuttal:

Meta-review: The paper proposes multi-model decoding strategy to reduce hallucinations in LLMs over several benchmarks 
A good number of experiments support the claims. 

The initial reviews suggested the paper has enough contributions and there were a good number of points that needed to be addressed. Reviewers acknowledge the effort made during the rebuttal phase to improve the quality of the paper and addressing the concerns. All reviewers raised their score leaning towards accepting the paper. 
After reading reviews and comments, AC agrees.
Decision: Accept (poster)