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

arXiv: https://arxiv.org/abs/2601.05144 · HTML: https://mlsanity.com/paper/2601.05144/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning.
- Builds on 60 of its 73 references that are in the map.
- First posted on arXiv 8 Jan 2026.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)
- LLM safety and security / [Watermarking generated content and models](https://mlsanity.com/safety/watermarking-generated-content-and-models/)

## Builds on (most cited first, 30 of 60)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [BERTScore: Evaluating Text Generation with BERT](https://mlsanity.com/paper/1904.09675/) (2019)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Inference-Time Intervention: Eliciting Truthful Answers from a Language Model](https://mlsanity.com/paper/2306.03341/) (2023)
- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [A Watermark for Large Language Models](https://mlsanity.com/paper/2301.10226/) (2023)
- [A Comprehensive Overview of Large Language Models](https://mlsanity.com/paper/2307.06435/) (2023)
- [Large Language Models for Information Retrieval: A Survey](https://mlsanity.com/paper/2308.07107/) (2023)
- [Provable Robust Watermarking for AI-Generated Text](https://mlsanity.com/paper/2306.17439/) (2023)
- [Large Language Models in Finance: A Survey](https://mlsanity.com/paper/2311.10723/) (2023)
- [Light-R1: Curriculum SFT, DPO and RL for Long COT from Scratch and Beyond](https://mlsanity.com/paper/2503.10460/) (2025)
- [Imitate, Explore, and Self-Improve: A Reproduction Report on Slow-thinking Reasoning Systems](https://mlsanity.com/paper/2412.09413/) (2024)
- [Who Wrote this Code? Watermarking for Code Generation](https://mlsanity.com/paper/2305.15060/) (2023)
- [Adversarial Watermarking Transformer: Towards Tracing Text Provenance with Data Hiding](https://mlsanity.com/paper/2009.03015/) (2020)
- [LawBench: Benchmarking Legal Knowledge of Large Language Models](https://mlsanity.com/paper/2309.16289/) (2023)
- [A Semantic Invariant Robust Watermark for Large Language Models](https://mlsanity.com/paper/2310.06356/) (2023)
- [A Survey of Text Watermarking in the Era of Large Language Models](https://mlsanity.com/paper/2312.07913/) (2023)
- [Unbiased Watermark for Large Language Models](https://mlsanity.com/paper/2310.10669/) (2023)
- [MarkLLM: An Open-Source Toolkit for LLM Watermarking](https://mlsanity.com/paper/2405.10051/) (2024)
- [A Robust Semantics-based Watermark for Large Language Model against Paraphrasing](https://mlsanity.com/paper/2311.08721/) (2023)
- [An Entropy-based Text Watermarking Detection Method](https://mlsanity.com/paper/2403.13485/) (2024)
- [Adaptive Text Watermark for Large Language Models](https://mlsanity.com/paper/2401.13927/) (2024)
- [An Unforgeable Publicly Verifiable Watermark for Large Language Models](https://mlsanity.com/paper/2307.16230/) (2023)
- [Advancing Beyond Identification: Multi-bit Watermark for Large Language Models](https://mlsanity.com/paper/2308.00221/) (2023)
- [A Resilient and Accessible Distribution-Preserving Watermark for Large Language Models](https://mlsanity.com/paper/2310.07710/) (2023)

## Built on by (most cited first, 3 of 3)

- [A Visual Semantic Adaptive Watermark grounded by Prefix-Tuning for Large Vision-Language Model](https://mlsanity.com/paper/2601.07291/) (2026)
- [Decoding by Perturbation: Mitigating MLLM Hallucinations via Dynamic Textual Perturbation](https://mlsanity.com/paper/2604.12424/) (2026)
- [Beyond Semantic Narrowing: Robust and Efficient LLM Watermarking with Hamming Neighborhoods](https://mlsanity.com/paper/2609.37218/) (2026)

## Abstract (arXiv)

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.