The growing deployment of Large Language Models (LLMs) has raised concerns about their misuse in generating harmful or deceptive content. To address this issue, watermarking methods have been proposed to embed identifiable multi-bit messages into generated text for misuse tracing. However, existing methods often suffer from a fundamental trade-off between text quality and decoding accuracy. In particular, they have to restrict the size of the preferred token set (i.e., green list) during encoding to maintain a detectable watermark signal for decoding, which inevitably degrades generation quality. To improve this trade-off, we propose a novel message encoding paradigm called majority bit-aware encoding, which relaxes the watermark signal strength from the green list size. This strategy allows for a strong watermark signal to be preserved in generated texts even when using a large green list. We introduce two instantiations of this paradigm: MajorMark and MajorMark+, where the latter is specifically optimized for long messages. Extensive experiments on state-of-the-art LLMs demonstrate that our methods achieve higher decoding accuracy and superior text quality compared to prior baselines. The code is at https://github.com/JiiahaoXU/MajorMark.
Figures & tables
Method
Encoding
Decoding
Em[γ]
×∣x∣
Eff.?
CTWL ctwl †
−
2b
✗
CycleShift cycleshift
=0.25
2b
✗
DepthW depthw
=0.50
2b
✗
RSBH rsbh ‡
=0.50
2d
✓
MPAC mpac
=0.25
1
✓
Table 1: Comparison of representative multi-bit LLM watermarking methods. Em[γ] denotes the expected green list ratio over all possible messages. ×∣x∣ indicates that the decoding process requires how many enumerations over all tokens in the input text x . “Eff.?” reflects whether the decoding procedure is computationally efficient.
Figure 1: Impact of green list ratio γ on the utility of watermarked text (right) and the decoding accuracy (left).
Figure 2: An overview of the majority bit-aware encoding process of MajorMark and MajorMark + .
Figure 3: Occurrence distributions for candidate λ (0 or 1). Distribution produced by the correct λ exhibits significant skewness.
Method
δ=2
δ=4
δ=6
Avg. BA ↑
Avg. PPL ↓
BA ↑
PPL ↓
Top- 5↑
BA ↑
PPL ↓
Top- 5↑
BA ↑
PPL ↓
Top- 5↑
Message length b=8
CycleShift
100.00
5.09
90.72
100.00
8.64
81.43
100.00
15.44
75.65
100.00
9.72
DepthW
95.62
4.53
91.65
100.00
8.24
79.53
100.00
25.49
61.13
98.54
12.75
MPAC
99.38
5.03
90.41
100.00
8.74
81.44
100.00
16.06
74.52
99.79
9.94
RSBH
100.00
4.80
91.19
100.00
6.36
89.30
100.00
8.66
86.87
100.00
6.61
Table 2: Comparison of methods across various message lengths and watermarking biases. The PPL of non-watermarked text is 3.81 , serving as a lower bound for the PPL of all watermarked texts.
Figure 4: BA of different methods under varying numbers of observed tokens T with b=64 .
Figure 5: BA and PPL of methods with increasing message length b∈{32,40,48,56,64} with δ=4 .
Method
LLaMA- 3.1 - 8 B
Qwen 3 - 8 B
PPL ↓
BA ↑
PPL ↓
BA ↑
MPAC
8.34
97.72
5.65
92.66
StealthInk
4.83
83.84
3.50
49.31
BiMark
8.39
99.47
5.05
96.66
MajorMark
6.79
98.41
4.91
96.91
MajorMark +
6.51
99.81
4.75
98.50
Table 3: Evaluation on recent public LLMs with 100 users.
Figure 6: BA of different methods under Copy-Paste and Paraphrase attacks.
Method
PPL ↓
BA ↑
CharP
SenS
MPAC
6.36
81.88
95.31
RSBH
5.47
78.28
93.25
MajorMark
5.31
82.84
94.97
MajorMark +
5.19
81.56
96.72
Table 4: Robustness evaluation under character-level perturbation (CharP) and sentence shuffling (SenS).
Method
Enc. (s)
Dec. (s)
BA ↑
DepthW
37.87
≈8.89×108 (Est.)
-
MPAC
36.13
0.13
89.22
RSBH
36.06
25.56
89.38
MajorMark
36.58
2.18
96.74
MajorMark +
36.85
12.70
97.81
Table 5: Comparison of runtime (in seconds) and BA. The decoding time for DepthW is estimated.
Method
δ=2
δ=4
Avg. BA ↑
Avg. PPL ↓
BA ↑
PPL ↓
BA ↑
PPL ↓
KMeans
96.74
4.43
99.06
6.32
97.90
5.38
AC
94.06
4.43
99.84
6.32
96.95
5.38
GMM
92.81
4.43
99.84
6.32
96.33
5.38
r=1
95.94
4.74
100.00
6.55
97.97
5.65
r=2
97.81
4.49
100.00
6.05
98.91
5.27
Table 6: Ablation study of MajorMark (first three rows) and MajorMark + (last four rows), evaluating clustering methods and block sizes, respectively.
Appendix figures & tables11 assets
Supplementary material from the paper’s appendix.
Appendix
Symbol
Description
γ
The green list ratio
m
The binary multi-bit message
mi
The i -th bit of the message m
b
The length of message m
f
The large language model
xp
The input prompt
Appendix
Table 7: Notation table.
Model
Method
δ=2
δ=4
Avg. BA ↑
Avg. PPL ↓
Avg. Top- 5↑
BA ↑
PPL ↓
Top- 5↑
BA ↑
PPL ↓
Top- 5↑
Message length b=32
Qwen 2.5 - 7 B
MajorMark
96.25
6.69
86.99
99.22
8.49
85.29
97.74
7.59
86.14
MajorMark +
98.75
6.31
88.39
100.00
8.85
84.77
99.38
7.58
86.58
Gemma- 2 B
MajorMark
96.41
7.02
87.16
99.06
9.80
83.38
97.74
8.41
85.27
MajorMark +
99.38
6.95
86.02
100.00
9.69
84.36
99.69
8.32
85.19
Appendix
Table 8: Performance of MajorMark and MajorMark + on Qwen 2.5 - 7 B, Gemma- 2 B, and LLaMA- 3.1 - 8 B with b∈{32,64} and δ∈{2,4} . The PPL for non-watermarked texts generated by Qwen 2.5 - 7 B, Gemma- 2 B, and LLaMA- 3.1 - 8 B are 4.97 , 5.71 , and 4.27 , respectively.
Method
δ=2
δ=4
δ=6
Avg. BA ↑
Avg. PPL ↓
Avg. Top- 5↑
BA ↑
PPL ↓
Top- 5↑
BA ↑
PPL ↓
Top- 5↑
BA ↑
PPL ↓
Top- 5↑
Message length b=32
MPAC
86.56
4.77
91.26
97.34
9.23
81.86
99.38
15.08
76.41
94.43
9.69
83.18
RSBH
84.53
4.68
92.47
96.56
6.43
89.98
97.66
8.64
88.47
92.92
6.58
90.31
MajorMark
90.94
4.35
92.83
97.81
6.02
90.01
99.38
8.51
87.95
96.04
6.29
90.26
MajorMark +
92.03
4.09
93.85
99.38
5.63
91.16
100.00
7.96
88.90
97.14
5.89
91.30
Appendix
Table 9: Performance comparison of watermarking methods (MPAC, RSBH, MajorMark, and MajorMark + ) on the OpenGen dataset with message lengths b∈{32,64} and watermarking biases δ∈{2,4,6} .
Method
δ=2
δ=4
δ=6
Avg. BA ↑
Avg. PPL ↓
Avg. Top- 5↑
BA ↑
PPL ↓
Top- 5↑
BA ↑
PPL ↓
Top- 5↑
BA ↑
PPL ↓
Top- 5↑
Message length b=32
MPAC
88.44
4.29
92.18
98.75
9.28
80.54
99.69
14.91
75.30
95.63
9.49
82.67
RSBH
89.22
4.23
93.31
97.66
6.33
88.98
97.66
7.78
87.78
94.85
6.11
90.02
MajorMark
91.41
4.12
93.24
98.28
5.98
89.60
99.53
7.71
87.70
96.41
5.94
90.18
MajorMark +
96.72
4.21
93.37
100.00
5.83
90.44
100.00
7.40
88.92
98.91
5.81
90.91
Appendix
Table 10: Performance comparison of watermarking methods (MPAC, RSBH, MajorMark, and MajorMark + ) on the Essays dataset with message lengths b∈{32,64} and watermarking biases δ∈{2,4,6} .
Method
δ=4
δ=6
Avg. BA ↑
Avg. PPL ↓
Avg. Top- 5↑
BA ↑
PPL ↓
Top- 5↑
BA ↑
PPL ↓
Top- 5↑
Message length b=32
MPAC
84.69
4.69
96.09
98.28
13.65
85.41
91.49
9.17
90.75
RSBH
83.28
4.17
98.17
96.41
6.20
96.81
89.85
5.19
97.49
MajorMark
89.38
4.09
98.70
96.41
6.19
97.12
92.90
5.14
97.91
MajorMark +
91.88
3.91
98.72
98.44
5.52
97.51
95.16
4.72
98.12
Appendix
Table 11: Performance comparison of watermarking methods on the WritingPrompts dataset for the story generation task with message lengths b∈{32,64} and watermarking biases δ∈{4,6} .
Method
δ=4
δ=6
Avg. BA ↑
Avg. PPL ↓
Avg. Top- 5↑
BA ↑
PPL ↓
Top- 5↑
BA ↑
PPL ↓
Top- 5↑
Message length b=32
MPAC
83.12
6.36
96.68
96.41
12.25
90.48
89.77
9.31
93.58
RSBH
85.00
5.81
98.83
97.34
8.07
97.24
91.17
6.94
98.04
MajorMark
88.12
5.72
99.02
95.78
7.70
98.00
91.95
6.71
98.51
MajorMark +
89.53
5.72
99.10
95.16
7.13
98.52
92.35
6.43
98.81
Appendix
Table 12: Performance comparison of watermarking methods on the CNN/DailyMail dataset for the text summarization task with message lengths b∈{32,64} and watermarking biases δ∈{4,6} .
Metric
MajorMark +
BiMark
W Statistic
p -value
PPL
4.75±0.95
5.05±1.23
1633.0
0.00108
BA
98.50±4.41
96.66±4.66
1094.0
0.00002
Appendix
Table 13: Statistical significance test over 100 users on Qwen 3 - 8 B. We report the mean and standard deviation of each metric across users.
Method
δ=2
δ=4
δ=6
MPAC
0.8376/0.33/0.29
0.8210/0.28/0.25
0.8105/0.26/0.22
RSBH
0.8384/0.35/0.31
0.8316/0.33/0.29
0.8234/0.30/0.26
MajorMark
0.8415/0.37/0.33
0.8305/0.33/0.28
0.8269/0.31/0.28
MajorMark +
0.8449/0.36/0.32
0.8381/0.34/0.29
0.8311/0.33/0.29
Appendix
Table 14: Semantic and lexical fidelity (BERTScore ↑ / ROUGE-1 ↑ / ROUGE-Lsum ↑ ) for different bias values δ with b=32 .
Method
TPR@1%FPR ↑
TPR@5%FPR ↑
MajorMark
98.00
99.00
MajorMark +
97.00
100.00
Appendix
Table 15: Detection performance under low-FPR settings with message length b=32 .
Figure 7: Pareto comparison under different (r,δ) combinations.
δ
hλ/b=71.88%
hλ/b=81.25%
2
(4.06,85.62)
(4.09,80.16)
4
(4.89,97.66)
(4.39,96.88)
6
(5.90,100.00)
(4.91,100.00)
8
(6.71,100.00)
(5.54,99.69)
Appendix
Table 16: Impact of watermarking bias δ under different message imbalance rates.
Multi-bit watermarking has emerged as a promising solution for embedding imperceptible binary messages into Large Language Model (LLM)-generated text, enabling reliable attribution and tracing of malicious usage of LLMs. Despite recent progress, existing methods still face key limitations: some become computationally infeasible for large messages, while others suffer from a poor trade-off between text quality and decoding accuracy. Moreover, the decoding accuracy of existing methods drops significantly when the number of tokens in the generated text is limited, a condition that frequently arises in practical usage. To address these challenges, we propose XMark, a novel method for encoding and decoding binary messages in LLM-generated texts. The unique design of XMark's encoder produces a less distorted logit distribution for watermarked token generation, preserving text quality, and also enables its tailored decoder to reliably recover the encoded message with limited tokens. Extensive experiments across diverse downstream tasks show that XMark significantly improves decoding accuracy while preserving the quality of watermarked text, outperforming prior methods. The code is at https://github.com/JiiahaoXU/XMark.
Jiahao Xu, Rui Hu, Olivera Kotevska +1
University of Nevada, Reno · Oak Ridge National Laboratory
Watermarking methods embed imperceptible and verifiable signals into text generated by large language models (LLMs). Existing approaches include zero-bit schemes for distinguishing synthetic text from human writing and multi-bit schemes for embedding metadata. However, current multi-bit watermarking methods do not allow selective disclosure: verifying any part of the watermark requires revealing the entire embedded message. This lack of control leads to unnecessary information exposure and raises privacy concerns. We propose Hierarchical Vocabulary Routing (HeRo), a watermarking framework that enables selective disclosure of embedded metadata. The method recursively partitions the vocabulary and distributes watermark information across hierarchical layers, so that different verifiers can decode only the portions of the payload corresponding to their access level. We show that the proposed scheme preserves the unbiasedness of the underlying sampling process and thus maintains text quality. Experiments demonstrate that our framework supports fine-grained access control while achieving high detection accuracy and low latency. Code is available at https://github.com/xuyangc03/hero-watermark.
With LLM watermarking already being deployed commercially, practical applications increasingly require multibit watermarks that encode more complex payloads, such as user IDs or timestamps, into the generated text. In this work, we propose a fundamentally new approach for multibit watermarking: introducing binomial encoding to directly encode every bit of the payload at every token position. We complement our approach with a stateful encoder that during generation dynamically redirects encoding pressure toward underencoded bits. Our evaluation against 8 baselines on up to 64-bit payloads shows that our scheme achieves superior message accuracy and robustness, with the gap to baseline methods widening in more relevant settings (i.e., large payloads and low-distortion regimes). At the same time, we challenge prior works' evaluation metrics, highlighting their lack of practical insights, and introduce per-bit confidence scoring as a practically relevant metric for evaluating multibit LLM watermarks.