Beyond Heuristic Tuning: Power-Calibrated LLM Watermarking

Logit-based watermarking is a widely used mechanism for identifying LLM generated content, yet its effectiveness is governed by a fundamental trade-off between detectability and semantic distortion. Existing analyses provide limited guidance for principled hyperparameter selection, leaving practical deployments reliant on heuristic tuning. In this work, we develop a power-calibrated statistical framework that establishes explicit quantitative relationships between watermark hyperparameters, detection power, and distortion. This characterization transforms watermark design into a guided optimization problem. Building on these results, we derive practical parameter selection procedures that achieve optimal trade-offs under constraints. Extensive experiments across multiple language models and datasets validate the theory and demonstrate that the proposed framework consistently identifies Pareto-optimal points.

AI systems can now produce long, fluent text, making it harder to tell when text was generated by a model. One common response is to add a watermark: a subtle pattern inserted during generation that a detector can later check. Existing watermarking systems usually rely on experience to choose how strong that pattern should be, a stronger pattern can make text easier to detect but may also reduce text quality. Our work turns this choice into a statistical calibration problem. We derive formulas that connect the watermark settings to the chance of detecting the watermark and to the amount of distortion introduced into the generated text. These formulas let users choose parameters that meet a desired detection reliability while keeping the watermark as unmodified as possible. We also test the method across several language models and datasets, including a larger model, and find that it consistently identifies better trade-offs than heuristic tuning. This matters because practical watermarking should be detectable, predictable, transparent, and minimally disruptive to the text being generated.