RMCW: A Deletion-Robust Watermark Based on Reed--Muller Codes for Language Models

Yi Wang; Baicheng Chen; Yu Wang; Jian Zhao; Yilei Chen; Tianxing He

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arXiv · 2610.02817

RMCW: A Deletion-Robust Watermark Based on Reed--Muller Codes for Language Models

Yi Wang·Baicheng Chen·Yu Wang·Jian Zhao·Yilei Chen·Tianxing He

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Abstract

Large Language Model (LLM) watermarking provides a lightweight mechanism for identifying text generated by a specific model, but its robustness remains fragile under post-processing attacks. Deletion attacks are particularly challenging because they shift token positions and break the alignment between observed tokens and their original watermark positions. We propose Reed--Muller Code Watermarking (RMCW), an LLM watermarking method based on Reed--Muller codes. In contrast to global codeword recovery, RMCW searches for surviving local algebraic structure, leveraging the Reed--Solomon consistency induced by affine-line restrictions of Reed--Muller codewords. During generation, RMCW injects a Reed--Muller structure into the sequence via a secret-keyed vocabulary partition. During detection, it maps the given text to keyed vocabulary bins and tests local subsequences for low-degree Reed--Solomon consistency using Berlekamp--Welch tests. Experiments on C4 and ELI5 datasets with OPT-1.3B and Llama-3.1-8B-Instruct show that RMCW preserves strong clean-text detectability and outperforms or matches the baseline methods under several deletion and rewriting attacks. Our code is available at https://github.com/BaichengDanny/RMCW.

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Yi Wang, Baicheng Chen, Yu Wang, Jian Zhao, Yilei Chen, Tianxing He. 2026-10-02. RMCW: A Deletion-Robust Watermark Based on Reed--Muller Codes for Language Models. https://arxiv.org/abs/2610.02817

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