Statistical watermarking techniques are well-established for sequentially decoded language models (LMs). However, these techniques cannot be directly applied to order-agnostic LMs, as the tokens in order-agnostic LMs are not generated sequentially. In this work, we introduce Pattern-mark, a pattern-based watermarking framework specifically designed for order-agnostic LMs. We develop a Markov-chain-based watermark generator that produces watermark key sequences with high-frequency key patterns. Correspondingly, we propose a statistical pattern-based detection algorithm that recovers the key sequence during detection and conducts statistical tests based on the count of high-frequency patterns. Our extensive evaluations on order-agnostic LMs, such as ProteinMPNN and CMLM, demonstrate Pattern-mark's enhanced detection efficiency, generation quality, and robustness, positioning it as a superior watermarking technique for order-agnostic LMs.
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