DGMark: Dual-Granularity Composite Entropy for Robust Vocabulary Partitioning in Vision-Language Model Watermarking

Watermarking large vision-language models embeds a detectable signal into generated text by dynamically partitioning the vocabulary into green and red lists at each decoding step, using a single entropy value to size the partition. This design has two shortcomings. The entropy-modulated ratio is rounded to an integer list size, and when the ratio is small relative to the vocabulary, the rounded size collapses to zero, silently discarding the semantic-critical subset and degrading the mechanism to a random partition; separately, at genuinely low-entropy steps, additively biasing green-list logits overrides the model's already-concentrated top-1 preference, distorting the output distribution precisely where the model is most confident. We propose two lightweight, training-free mechanisms that address these gaps while keeping the underlying LVLM frozen. A dual-granularity composite entropy signal fuses normalized Shannon entropy with the top-1/top-2 probability margin and the Gini coefficient, paired with a list-size floor that provably keeps the semantic-critical subset non-empty at every step without disturbing the continuous modulation elsewhere. A low-entropy rejection sampling scheme replaces additive logit biasing with resampling directly from the original distribution at low-entropy steps, preserving natural confidence structure while still enforcing a detectable signal. We evaluate on Qwen3-VL-8B-Instruct using the AMBER benchmark, reporting perplexity, BLEU, and BERTScore alongside entropy-bucketed statistics of the adaptive green-list ratio. Together, these two mechanisms fix the partition-collapse and low-entropy distortion failure modes in attention-guided LVLM watermarking, improving semantic fidelity without sacrificing detectability or efficiency.