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Optimizing Watermarks for Large Language Models
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Formulates the identifiability-vs-text-quality trade-off of green-red LLM watermarks as a multi-objective optimization and derives Pareto-optimal "OPT" watermarks that outperform KGW, DiP and ITS on the test-text trade-off.
Problem
Watermarks for LLM-generated text trade off identifiability (detection power) against degradation of text quality; there is no systematic way to optimize this trade-off within the class of robust, efficient green-red split watermarks.
Approach
Translate the test-text trade-off into a bi-objective problem (maximize expected green-list count, minimize expected log-perplexity shift) over a general class of shift functions; the Pareto-optimal solution shifts probability fully to green tokens whenever the per-token expected damage B is below a threshold beta, and leaves the distribution unchanged otherwise.
Key results
- OPT watermark attains the derived Pareto optimal bound and outperforms KGW, DiP and ITS on the expected green-count vs log-perplexity trade-off with OPT-1.3B.
- On summarization (BART-large) and translation (mBART), KGW outperforms OPT on ROUGE-1 vs power of the test, showing optimality for one text-quality metric does not transfer to another.
- The binomial assumption behind the power-of-test optimality breaks down: green-token events are positively correlated, with KL divergence increasing with watermark strength.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use OPT instead of KGW, DiP, or ITS | OPT-1.3B watermarking · C4 | test-text trade-off using expected green-list tokens and expected log-perplexity | Helped |
| Use OPT instead of KGW | BART-large watermarking · CNN-DM text summarization | test-text trade-off using test power and ROUGE-1 | Hurt |
| Use OPT instead of KGW | Multilingual BART watermarking · WMT 2016 English-to-Romanian | test-text trade-off using test power and ROUGE-1 | Hurt |
| Use OPT instead of OPT′ | OPT watermarking · OPT-350m | test-text trade-off using expected log-perplexity | No clear effect |
| Use OPT′ instead of OPT | OPT watermarking · OPT-350m | test-text trade-off using expected log-perplexity squared plus between-token var | Helped |
| Apply KGW or OPT watermarking | LLM text generation · C4 | bigram and trigram diversity | Hurt |
| Use OPT rather than other watermarks | LLM text generation · C4 | bigram and trigram diversity | Hurt |
| Use DiP rather than the original LLM | LLM text generation · C4 | bigram and trigram diversity | Hurt |
| Use DiP rather than the original LLM | LLM text generation · CNN-DM summarization and WMT 2016 translation | identifiability | Hurt |
| Use ITS with beam search | LLM text generation · CNN-DM summarization and WMT 2016 translation | ROUGE-1 | Hurt |
| Use OPT′ instead of OPT | LLM text generation · OPT-350m | expected log-perplexity | No clear effect |
| Use stronger watermarks | KGW and OPT · C4 | dependence between green-token events | Hurt |
Surprising findings
- OPT watermark is outperformed by KGW on ROUGE-1-based text quality for summarization and translation, so optimized watermarks may not be superior under other metrics.
- OPT reduces bi- and tri-gram diversity more than other watermarks, a potential disadvantage.
Limitations
- Binomial independence assumption is violated for stronger watermarks, undermining the Pareto optimality guarantee for power of the test.
- Expected green-count and log-perplexity are used as proxies; OPT underperforms KGW on ROUGE-1 for summarization and translation.
- Experiments are limited to short sequences (T=30) and small OPT models.
Experimental setup
Datasets: C4 CNN-DM WMT 2016
Benchmarks: C4 news continuation CNN-DM WMT 2016 English-Romanian
Metrics: expected green-list tokens log-perplexity power of the test ROUGE-1 n-gram diversity KL divergence
Baselines: KGW hard watermark DiP ITS
Builds on: KGW watermark distribution-preserving watermark inverse transform sampling watermark
Closest papers by meaning
- Provable Robust Watermarking for AI-Generated Text (ICLR 2024 · similarity 0.90)
- Theoretically Grounded Framework for LLM Watermarking: A Distribution-Adaptive Approach (NeurIPS 2025 · similarity 0.90)
- Unbiased Watermark for Large Language Models (ICLR 2024 · similarity 0.89)
- Learning to Watermark: A Selective Watermarking Framework for Large Language Models via Multi-Objective Optimization (NeurIPS 2025 · similarity 0.88)
- Token-Specific Watermarking with Enhanced Detectability and Semantic Coherence for Large Language Models (ICML 2024 · similarity 0.88)
- Inevitable Trade-off between Watermark Strength and Speculative Sampling Efficiency for Language Models (NeurIPS 2024 · similarity 0.88)
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