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MorphMark: Flexible Adaptive Watermarking for Large Language Models

Zongqi Wang, Tianle Gu, Baoyuan Wu, Yujiu Yang

TL;DR

The paper tackles the fundamental trade-off in LLM watermarking between detectability and text quality. It formalizes this as a multi-objective optimization and identifies the cumulative green-list probability $P_G$ as a key driver, showing that the optimal watermark strength $r^*$ increases with $P_G$. It then introduces MorphMark, a dynamic, model-agnostic watermarking method that adapts $r$ based on $P_G$, and demonstrates improved effectiveness-quality trade-offs, robustness, and efficiency across diverse models and tasks. Empirical results substantiate MorphMark's practical benefits, including detection performance without extra memory overhead in detection, making it a flexible solution for real-world deployment.

Abstract

Watermarking by altering token sampling probabilities based on red-green list is a promising method for tracing the origin of text generated by large language models (LLMs). However, existing watermark methods often struggle with a fundamental dilemma: improving watermark effectiveness (the detectability of the watermark) often comes at the cost of reduced text quality. This trade-off limits their practical application. To address this challenge, we first formalize the problem within a multi-objective trade-off analysis framework. Within this framework, we identify a key factor that influences the dilemma. Unlike existing methods, where watermark strength is typically treated as a fixed hyperparameter, our theoretical insights lead to the development of MorphMarka method that adaptively adjusts the watermark strength in response to changes in the identified factor, thereby achieving an effective resolution of the dilemma. In addition, MorphMark also prioritizes flexibility since it is a model-agnostic and model-free watermark method, thereby offering a practical solution for real-world deployment, particularly in light of the rapid evolution of AI models. Extensive experiments demonstrate that MorphMark achieves a superior resolution of the effectiveness-quality dilemma, while also offering greater flexibility and time and space efficiency.

MorphMark: Flexible Adaptive Watermarking for Large Language Models

TL;DR

The paper tackles the fundamental trade-off in LLM watermarking between detectability and text quality. It formalizes this as a multi-objective optimization and identifies the cumulative green-list probability as a key driver, showing that the optimal watermark strength increases with . It then introduces MorphMark, a dynamic, model-agnostic watermarking method that adapts based on , and demonstrates improved effectiveness-quality trade-offs, robustness, and efficiency across diverse models and tasks. Empirical results substantiate MorphMark's practical benefits, including detection performance without extra memory overhead in detection, making it a flexible solution for real-world deployment.

Abstract

Watermarking by altering token sampling probabilities based on red-green list is a promising method for tracing the origin of text generated by large language models (LLMs). However, existing watermark methods often struggle with a fundamental dilemma: improving watermark effectiveness (the detectability of the watermark) often comes at the cost of reduced text quality. This trade-off limits their practical application. To address this challenge, we first formalize the problem within a multi-objective trade-off analysis framework. Within this framework, we identify a key factor that influences the dilemma. Unlike existing methods, where watermark strength is typically treated as a fixed hyperparameter, our theoretical insights lead to the development of MorphMarka method that adaptively adjusts the watermark strength in response to changes in the identified factor, thereby achieving an effective resolution of the dilemma. In addition, MorphMark also prioritizes flexibility since it is a model-agnostic and model-free watermark method, thereby offering a practical solution for real-world deployment, particularly in light of the rapid evolution of AI models. Extensive experiments demonstrate that MorphMark achieves a superior resolution of the effectiveness-quality dilemma, while also offering greater flexibility and time and space efficiency.
Paper Structure (30 sections, 1 theorem, 29 equations, 9 figures, 6 tables, 1 algorithm)

This paper contains 30 sections, 1 theorem, 29 equations, 9 figures, 6 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Methodology
  4. Multi-objective Trade-off Framework
  5. Adaptive Watermark
  6. Experiments
  7. Experimental Setup
  8. Overall Performance
  9. Performance on Robustness
  10. Performance on Text Quality
  11. Ablation Study
  12. Further Analyses
  13. Different Sampling Parameters
  14. In-Depth Analysis of $P_G$ Distribution
  15. Evaluation in Low-Entropy Scenarios
  16. ...and 15 more sections

Key Result

Theorem 1

Consider the process of sampling a token from the watermarked probability distribution described above, for any given $\omega > 0$, there exists an optimal $r^* \in (0,1)$ that maximizes $\mathcal{F}$. Moreover, the optimal $r^*$ is positively correlated with $P_G$, i.e., $\frac{\partial r^*}{\parti

Figures (9)

  • Figure 1: Visualization of $\mathcal{F}$ across different $P_G$ and $r$. The vertical axis represents $\mathcal{F}$. A dashed dark gray line is used to indicate the optimal $r$ (i.e., $r^*$) that maximizes $\mathcal{F}$ for a fixed $P_G$. We can observe that as $P_G$ decreases, $r^*$ also decreases.
  • Figure 2: An example illustrating the adaptive mechanism of MorphMark. During token generation, the vocabulary is split into green and red lists. Since the split is based on the preceding tokens and user-defined keys, different tokens and users will have different splits. MorphMark adjusts the watermark strength based on the total probability of green tokens. High strength is applied when this probability is high, while low strength is used when this probability is low.
  • Figure 3: Robustness performance of each watermarking method under various attack scenarios.
  • Figure 4: Text quality on downstream tasks.
  • Figure 5: Parameter ablation study of MorphMark. In (a), (b), and (c), we conduct an ablation study on $k$ across different variants of MorphMark, where the x-axis represents $k$. In (d), we perform an ablation study on the watermarking threshold, where the x-axis represents $p_0$.
  • ...and 4 more figures

Theorems & Definitions (1)

  • Theorem 1