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Distilling the Thought, Watermarking the Answer: A Principle Semantic Guided Watermark for Large Reasoning Models

Shuliang Liu, Xingyu Li, Hongyi Liu, Yibo Yan, Bingchen Duan, Qi Zheng, Dong Fang, Lingfeng Su, Xuming Hu

TL;DR

ReasonMark addresses watermarking for reasoning-intensive LLMs by decoupling the thinking and answering phases. It distills semantic anchors from the thinking trace into a Principal Semantic Vector (PSV) via Critical Tokens and PCA, then uses PSV to guide a semantically-adaptive watermark during the answer phase. The approach combines Global Causal Contribution (GCC) and Competitive Persistence Scoring (CPS) to identify CTs and creates a unified Criticality Score (CS) to select them. Experiments across text generation, translation, and mathematical reasoning show improved text quality, stronger watermark detectability, and robustness to attacks with negligible latency, demonstrating practical viability for trusted deployment.

Abstract

Reasoning Large Language Models (RLLMs) excelling in complex tasks present unique challenges for digital watermarking, as existing methods often disrupt logical coherence or incur high computational costs. Token-based watermarking techniques can corrupt the reasoning flow by applying pseudo-random biases, while semantic-aware approaches improve quality but introduce significant latency or require auxiliary models. This paper introduces ReasonMark, a novel watermarking framework specifically designed for reasoning-intensive LLMs. Our approach decouples generation into an undisturbed Thinking Phase and a watermarked Answering Phase. We propose a Criticality Score to identify semantically pivotal tokens from the reasoning trace, which are distilled into a Principal Semantic Vector (PSV). The PSV then guides a semantically-adaptive mechanism that modulates watermark strength based on token-PSV alignment, ensuring robustness without compromising logical integrity. Extensive experiments show ReasonMark surpasses state-of-the-art methods by reducing text Perplexity by 0.35, increasing translation BLEU score by 0.164, and raising mathematical accuracy by 0.67 points. These advancements are achieved alongside a 0.34% higher watermark detection AUC and stronger robustness to attacks, all with a negligible increase in latency. This work enables the traceable and trustworthy deployment of reasoning LLMs in real-world applications.

Distilling the Thought, Watermarking the Answer: A Principle Semantic Guided Watermark for Large Reasoning Models

TL;DR

ReasonMark addresses watermarking for reasoning-intensive LLMs by decoupling the thinking and answering phases. It distills semantic anchors from the thinking trace into a Principal Semantic Vector (PSV) via Critical Tokens and PCA, then uses PSV to guide a semantically-adaptive watermark during the answer phase. The approach combines Global Causal Contribution (GCC) and Competitive Persistence Scoring (CPS) to identify CTs and creates a unified Criticality Score (CS) to select them. Experiments across text generation, translation, and mathematical reasoning show improved text quality, stronger watermark detectability, and robustness to attacks with negligible latency, demonstrating practical viability for trusted deployment.

Abstract

Reasoning Large Language Models (RLLMs) excelling in complex tasks present unique challenges for digital watermarking, as existing methods often disrupt logical coherence or incur high computational costs. Token-based watermarking techniques can corrupt the reasoning flow by applying pseudo-random biases, while semantic-aware approaches improve quality but introduce significant latency or require auxiliary models. This paper introduces ReasonMark, a novel watermarking framework specifically designed for reasoning-intensive LLMs. Our approach decouples generation into an undisturbed Thinking Phase and a watermarked Answering Phase. We propose a Criticality Score to identify semantically pivotal tokens from the reasoning trace, which are distilled into a Principal Semantic Vector (PSV). The PSV then guides a semantically-adaptive mechanism that modulates watermark strength based on token-PSV alignment, ensuring robustness without compromising logical integrity. Extensive experiments show ReasonMark surpasses state-of-the-art methods by reducing text Perplexity by 0.35, increasing translation BLEU score by 0.164, and raising mathematical accuracy by 0.67 points. These advancements are achieved alongside a 0.34% higher watermark detection AUC and stronger robustness to attacks, all with a negligible increase in latency. This work enables the traceable and trustworthy deployment of reasoning LLMs in real-world applications.
Paper Structure (43 sections, 1 theorem, 21 equations, 5 figures, 6 tables)

This paper contains 43 sections, 1 theorem, 21 equations, 5 figures, 6 tables.

Table of Contents

  1. introdution
  2. Preliminary
  3. Related Work.
  4. Principle Semantic Vector Construction.
  5. Methodology
  6. Algorithmic Realization of PSV Construction $f_{\eta}$
  7. Criticality Score
  8. Global Causal Contribution (GCC).
  9. Competitive Persistence Scoring (CPS).
  10. Consolidated Criticality Score (CS).
  11. From Critical Tokens to Principal Semantic Vector
  12. Semantically-Adaptive Watermark Embedding $g_{\sigma}$ and $f_{\mu}$
  13. Dynamic Watermark Strength.
  14. Dynamic PSV Update.
  15. Watermark Detection.
  16. ...and 28 more sections

Key Result

Theorem 2.2

The optimal set of Critical Tokens, denoted $\mathcal{C}^* \subseteq \mathcal{V}$, is the set that maximizes a joint measure of causal influence and competitive significance, subject to a constraint $|\mathcal{C}| \leq K$ on its size: where $K$ is the maximum desired number of Critical Tokens, $\theta$ represents model parameters, and $\omega$ balances the two measures. The Causal Divergence $D_{

Figures (5)

  • Figure 1: ReasonMark identifies top-K critical tokens during the thinking phase (II.) and uses PCA (III.) to establish an initial Principal Semantic Vector (PSV). This semantic vector then guides the watermarking process (IV.) by dynamically adjusting the logits to favor semantically coherent green tokens and penalize disruptive ones.This enables the efficient generation of a semantically coherent watermarked sequence with a high proportion of green tokens (V.) by sampling only one time.
  • Figure 2: ROC curves under different attack methods for various watermarking approaches.
  • Figure 3: Visualization of $\beta_0$ and top-k.
  • Figure 4: Visualization of $\delta_0$ and $\delta_{\lambda}$.
  • Figure 5: PCA visualization of Critical Token embeddings for four cases from the C4 dataset, generated by the Qwen3 model as detailed in Appendix \ref{['app:case-study']}.

Theorems & Definitions (2)

  • Definition 2.1: Semantic Guidance via Principal Semantic Vector
  • Theorem 2.2: Optimal Representation of Critical Tokens