We demonstrate that while the current approaches for language model watermarking are effective for open-ended generation, they are inadequate at watermarking LM outputs for constrained generation tasks with low-entropy output spaces. Therefore, we devise SeqMark, a sequence-level watermarking algorithm with semantic differentiation that balances output quality, watermark detectability, and imperceptibility. It improves on the shortcomings of token-level watermarking algorithms that cause under-utilization of the sequence-level entropy available for constrained generation tasks. Moreover, we identify and improve upon the problem of region collapse, a different failure mode associated with prior sequence-level watermarking algorithms. This occurs because the pseudorandom partitioning of semantic space for watermarking in these approaches causes all high-probability outputs to collapse into either invalid or valid regions, leading to a trade-off in output quality and watermarking effectiveness. Instead, SeqMark differentiates the high-probable output subspace and partitions it into valid and invalid regions, ensuring the even spread of high-quality outputs among all the regions. On various constrained generation tasks like machine translation, abstractive summarization, and code generation, SeqMark substantially improves watermark detection accuracy (up to 28% increase in F1) while maintaining high generation quality.

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