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BiMarker: Enhancing Text Watermark Detection for Large Language Models with Bipolar Watermarks

Zhuang Li, Qiuping Yi, Zongcheng Ji, Yijian Lu, Yanqi Li, Keyang Xiao, Hongliang Liang

TL;DR

BiMarker tackles the challenge of distinguishing AI-generated text from human content by introducing a bipolar watermarking scheme for LLM outputs. It partitions generated text into a positive and a negative pole, applying a bias to green tokens in the positive pole and to red tokens in the negative pole, and detects watermarks via the difference in green-token counts between poles, with a z-score $z = \frac{|s|_{pG} - |s|_{nG} - \gamma T_p + (1-\gamma) T_n}{\sqrt{T\gamma(1-\gamma)}}$. Theoretical analysis shows a higher lower bound for the detection statistic than KGW and no increase in false positives, and BiMarker is orthogonal to entropy-based optimizations such as SWEET and EWD, enabling seamless integration. Empirical results across high- and low-entropy tasks demonstrate superior detection accuracy, robustness to back-translation, and compatibility with existing watermarking enhancements, suggesting a practical path to robust LLM watermarking in real-world settings.

Abstract

The rapid growth of Large Language Models (LLMs) raises concerns about distinguishing AI-generated text from human content. Existing watermarking techniques, like \kgw, struggle with low watermark strength and stringent false-positive requirements. Our analysis reveals that current methods rely on coarse estimates of non-watermarked text, limiting watermark detectability. To address this, we propose Bipolar Watermark (\tool), which splits generated text into positive and negative poles, enhancing detection without requiring additional computational resources or knowledge of the prompt. Theoretical analysis and experimental results demonstrate \tool's effectiveness and compatibility with existing optimization techniques, providing a new optimization dimension for watermarking in LLM-generated content.

BiMarker: Enhancing Text Watermark Detection for Large Language Models with Bipolar Watermarks

TL;DR

BiMarker tackles the challenge of distinguishing AI-generated text from human content by introducing a bipolar watermarking scheme for LLM outputs. It partitions generated text into a positive and a negative pole, applying a bias to green tokens in the positive pole and to red tokens in the negative pole, and detects watermarks via the difference in green-token counts between poles, with a z-score . Theoretical analysis shows a higher lower bound for the detection statistic than KGW and no increase in false positives, and BiMarker is orthogonal to entropy-based optimizations such as SWEET and EWD, enabling seamless integration. Empirical results across high- and low-entropy tasks demonstrate superior detection accuracy, robustness to back-translation, and compatibility with existing watermarking enhancements, suggesting a practical path to robust LLM watermarking in real-world settings.

Abstract

The rapid growth of Large Language Models (LLMs) raises concerns about distinguishing AI-generated text from human content. Existing watermarking techniques, like \kgw, struggle with low watermark strength and stringent false-positive requirements. Our analysis reveals that current methods rely on coarse estimates of non-watermarked text, limiting watermark detectability. To address this, we propose Bipolar Watermark (\tool), which splits generated text into positive and negative poles, enhancing detection without requiring additional computational resources or knowledge of the prompt. Theoretical analysis and experimental results demonstrate \tool's effectiveness and compatibility with existing optimization techniques, providing a new optimization dimension for watermarking in LLM-generated content.
Paper Structure (40 sections, 4 theorems, 30 equations, 8 figures, 4 tables, 1 algorithm)

This paper contains 40 sections, 4 theorems, 30 equations, 8 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Works
  3. Watermarking for Existing Texts
  4. Watermarking for LLMs
  5. Method
  6. Movitation
  7. Our Method
  8. Generating the Watermark.
  9. Detecting the watermark.
  10. Remark.
  11. Effect of Bipolar Watermark
  12. Applying BiMarker to SWEET and EWD.
  13. Experiments
  14. Tasks and Datasets.
  15. Main Results.
  16. ...and 25 more sections

Key Result

Theorem 3.1

Consider watermarked text sequences $s$ of $T$ tokens. Each sequence is produced by sequentially sampling a raw probability vector $p(t)$ from the language model, sampling a random green list of size $\gamma |V|$. The sequence $s$ is composed of a positive part $s_p$ and a negative part $s_n$. The l

Figures (8)

  • Figure 1: Illustration of the key idea of BiMarker: Adjust token bias by polarity during generation and detect by the green token difference between polarities.
  • Figure 2: Empirical Study of the Relationship Between the Number of Green Tokens in Human-Written Texts and the Number of Green Tokens in Watermarked Texts.
  • Figure 3: The relationship between watermark strength and accuracy under zero false positives (0/500). The left figure illustrates results with multinomial sampling, while the right figure depicts results using beam search with a beam size of 8.
  • Figure 4: Z-scores of Watermarked and Human Texts under Different Parameter Settings with multinomial sampling.
  • Figure 5: The Average Z-Score as a Function of Token Length ($T$) of the Generated Text with multinomial sampling.
  • ...and 3 more figures

Theorems & Definitions (4)

  • Theorem 3.1
  • Theorem 3.2
  • Lemma 1.1
  • Lemma 1.2