Watermarkability: Measuring and Improving Language-Model Compatibility with Logit-Based Watermarks

Zewei Deng, Mohamed Seif, Liyan Xie

Language-model watermarks can help identify model-generated text, encode provenance information, and detect post-generation edits. A broad class of logit-based watermarks increases the logits of a designated token set at each decoding step. Because a base model's native probability mass on this set varies across contexts, models, and watermark rules, the same logit bias can yield different adherence rates and increases in perplexity (PPL). We introduce watermarkability to characterize the compatibility between a model and the token sets requested by a watermark. At a target mass $τ$, we quantify this property through a watermarkability cost: the expected minimum KL divergence from the base-model distribution required to assign probability at least $τ$ to the requested set. A lower cost means that the model is more watermarkable for that request distribution. To reduce this cost, we propose a two-stage method. In the first stage, we train a target-set-conditioned low-rank adapter on unions drawn from a 16-way vocabulary partition to increase the requested set's probability mass. In the second stage, a closed-form controller applies the smallest remaining uniform logit bias needed…