Gamark: adaptive entropy-threshold watermarking via gaussian mixture modeling for large language models

Abstract

Existing generative watermarking methods rely on fixed or heuristic entropy thresholds in cross-task generation scenarios, leading to redundant watermark injection, detection noise, and degraded generation quality. To address these limitations, we propose GAMark, a Gaussian Mixture Model (GMM)-based semantics-aware Adaptive entropy threshold waterMarking framework. Motivated by the manifold hypothesis in the logits space, GAMark adopts an offline semantic modeling and online frozen inference paradigm. A GMM is trained offline to characterize multimodal latent semantic states, while during generation, entropy thresholds are dynamically synthesized via Bayesian posterior aggregation over semantic states, enabling automatic avoidance of low-entropy sensitive regions and effective watermark embedding in high-entropy regions. At the detection stage, we further introduce an entropy-weighted statistical test based on state inference, which improves robustness against noise introduced by the inclusion of semantically deterministic tokens. Extensive experiments demonstrate that GAMark consistently improves cross-task generation quality and functional correctness, while maintaining detection accuracy and enhancing watermark robustness and inference efficiency.