ArcMark: Multi-bit LLM Watermark via Optimal Transport

• URL: http://arxiv.org/abs/2602.07235v1
• Date: Fri, 06 Feb 2026 22:28:03 GMT
• Title: ArcMark: Multi-bit LLM Watermark via Optimal Transport
• Authors: Atefeh Gilani, Carol Xuan Long, Sajani Vithana, Oliver Kosut, Lalitha Sankar, Flavio P. Calmon,
• Abstract summary: We present the first capacity characterization of multi-bit watermarks.<n>We show that ArcMark outperforms competing multi-bit watermarks in terms of bit rate per token and detection accuracy.
• Score: 20.227686719113134
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Watermarking is an important tool for promoting the responsible use of language models (LMs). Existing watermarks insert a signal into generated tokens that either flags LM-generated text (zero-bit watermarking) or encodes more complex messages (multi-bit watermarking). Though a number of recent multi-bit watermarks insert several bits into text without perturbing average next-token predictions, they largely extend design principles from the zero-bit setting, such as encoding a single bit per token. Notably, the information-theoretic capacity of multi-bit watermarking -- the maximum number of bits per token that can be inserted and detected without changing average next-token predictions -- has remained unknown. We address this gap by deriving the first capacity characterization of multi-bit watermarks. Our results inform the design of ArcMark: a new watermark construction based on coding-theoretic principles that, under certain assumptions, achieves the capacity of the multi-bit watermark channel. In practice, ArcMark outperforms competing multi-bit watermarks in terms of bit rate per token and detection accuracy. Our work demonstrates that LM watermarking is fundamentally a channel coding problem, paving the way for principled coding-theoretic approaches to watermark design.

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