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. (2026b)) calibrates this signal against the model's sampling entropy through an explicit entropy budget, combining the stochasticity of Red-Green and the unbiasedness of Gumbel-max watermarks, and its accompanying report proposes a detector that sums pivotal statistics. We study when, and how efficiently, textGrain can be detected after human edits, modeled as a sparse mixture in which a fraction εn≍n−p of positions retain the watermark and token uncertainty decays as n−q. 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. This cost stems from textGrain's construction rather than from entropy calibration itself: an unbiased scheme with the same entropy loss remains detectable where textGrain is not. Second, perhaps surprisingly, this loss makes the sum detector optimal at the boundary when the number of transport columns is fixed, unlike for Gumbel-max. When the number of columns grows and the entropy budget does not vanish, the detectable region expands while that of the sum detector does not. Third, for a fixed edit fraction, we characterize the optimal exponential rate of type II error decay and show that the sum detector falls strictly short of it at every fixed alternative. 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.
Figures & tables
Figure 1
Watermark
Detection boundary
textGrain , fixed m
2p+2q=1
textGrain , growing m
2p+2q−min(s,q)=1
Gumbel-max
2p+q=1
Maximal coupling †
2p+q=1
Table 1: Detection boundaries in the (p,q) plane, where εn≍n−p , Δn≍n−q and, for growing m , mn≍ns . Both textGrain rows assume entropy fractions βn≳1 ; no test separates the hypotheses above the boundary, and consistent tests exist below it.
Watermarking provides a principled way to authenticate text generated by large language models (LLMs). In practice, however, the final text may be mixed-source, with watermark evidence surviving at only a subset of token positions after rewriting, insertion, deletion, or paraphrasing. Although prior work has studied global detection of watermark signals, when such signals can be localized remains unclear. We formulate watermark localization as a token-level multiple-testing problem based on pivotal statistics, with a latent indicator recording whether watermark dependence survives at each position. Under an asymptotic regime indexed by exponents for signal sparsity, next-token concentration, and effective-vocabulary growth, we derive a sharp boundary for global detection and phase transitions for discovery and classification within the class of coordinatewise pivot-based localization rules. We show that discovery is strictly harder than detection and that consistent classification is impossible across the parameter regime within this class. We then develop an adaptive thresholding method that does not require knowledge of the exponents or time-varying next-token distributions, but uses a data-driven estimate of the surviving watermark fraction. The method attains the optimal discovery boundary and near-optimal discovery power relative to homogeneous pivot-based rules. Simulations support the theoretical phase transitions, while experiments on model-generated texts demonstrate practical localization performance under common edit mechanisms.
We introduce TextSeal, a state-of-the-art watermark for large language models. Building on Gumbel-max sampling, TextSeal introduces dual-key generation to restore output diversity, along with entropy-weighted scoring and multi-region localization for improved detection. It supports serving optimizations such as speculative decoding and multi-token prediction, and does not add any inference overhead. TextSeal strictly dominates baselines like SynthID-text in detection strength and is robust to dilution, maintaining confident localized detection even in heavily mixed human/AI documents. The scheme is theoretically distortion-free, and evaluation across reasoning benchmarks confirms that it preserves downstream performance; while a multilingual human evaluation (6000 A/B comparisons, 5 languages) shows no perceptible quality difference. Beyond its use for provenance detection, TextSeal is also ``radioactive'': its watermark signal transfers through model distillation, enabling detection of unauthorized use.
As watermarking of LLM-generated text enters deployment, users increasingly need to check text whose source is unknown. Existing detectors read the watermark through a specific tokenizer or embedding pipeline, and even if all providers adopted the same watermarking method, differences in these representations would leave their watermarks incompatible, and the text alone does not reveal which representation produced it. We propose ByteMark, a unified watermarking scheme that defines its signal on the UTF-8 bytes of published text. Models with different tokenizers embed this signal under one public specification and key, and a single detector verifies the text from the text and key alone. When the tokenizer or embedding model of a baseline detector is replaced, its detection degrades sharply, whereas ByteMark, which uses neither, retains its detection rate; ByteMark also remains detectable when participating models continue or rewrite the text.