textGrain watermarking is harder to detect: can sum-tests still do it optimally?

Key points

• The recent textGrain watermark (Li et. al.1
• We study when, and how efficiently, textGrain can be detected after human edits, modeled as a sparse mixture in which a fraction $\varepsilonn\asymp n^{-p}$ of positions retain the watermark and token uncertainty decays as $n^{-q}$.1
• First, entropy calibration comes at a cost: the minimax detection boundary of textGrain is $p+q=1/2$, so its detectable region is strictly smaller than that of Gumbel-max and maximal-coupling watermarks, whose boundary is $2p+q=1$.1
• Finally, we propose a weighted multiscale binomial scan, valid in finite samples and needing no knowledge of the next-token distributions, entropy budget, or edit fraction; it attains every detection boundary above and the optimal exponent.1

Sources (1)

• [1]textGrain watermarking is harder to detect: can sum-tests still do it optimally?
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 13, 03:33 AM

  Watermarking embeds an imperceptible signal in text from large language models that is statistically detectable with a secret key.

  The recent textGrain watermark (Li et. al.

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