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Learning to Watermark: A Selective Watermarking Framework for Large Language Models via Multi-Objective Optimization
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Proposes Learning to Watermark (LTW), a selective LLM watermark where a lightweight MLP selector, trained with MGDA-based multi-objective loss, decides per token whether to apply KGW or Unigram watermarking, improving text quality while keeping detectability.
Problem
Watermarking LLM outputs trades off detectability against generated text quality; existing selective methods rely on hand-tuned entropy thresholds, and the watermark strength versus quality trade-off remains hard to balance.
Approach
A learned Selector Network (MLP) takes a SimCSE sentence embedding of recent tokens, current token entropy, and current watermark ratio to output a selection probability, thresholded by an adaptive ratio-dependent threshold; it is trained with two losses (quality and detectability) combined via MGDA to reach Pareto-optimal trade-offs.
Key results
- On OPT-6.7B under no attack, LTW-1 and LTW-0 reach AUROC 1.00000 and lower perplexity (13.62) than KGW (20.52) and SWEET (17.93).
- Under Dipper paraphrase attack on OPT-6.7B, LTW-0 achieves TPR@10 of 0.954 and AUROC 0.98326, versus 0.910 and 0.96987 for KGW.
- On GPT-J-6B, LTW-0 reduces perplexity to 9.56 compared with 16.55 for KGW, while LTW-1 gives the highest similarity (0.5286).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Apply selective watermarking to KGW (LTW-1) | KGW · OPT-6.7B | Perplexity: 20.5234 -> 13.6205 | Helped |
| Apply selective watermarking to Unigram (LTW-0) | Unigram · OPT-6.7B | Perplexity: 17.6761 -> 13.6238 | Helped |
| Apply selective watermarking to Unigram (LTW-0) | Unigram · GPT-J-6B | TPR@10 under Dipper attack: 0.944 -> 0.926 | Hurt |
| Apply selective watermarking to KGW (LTW-1) | KGW · OPT-6.7B | Similarity: 0.5472 -> 0.5701 | Helped |
| Use adaptive threshold rather than fixed threshold (ablation) | LTW · OPT-6.7B, watermark strengths δ = 1.5, 2, 2.5, 3, 3.5, and 4 | Z-score: 6.831 -> 6.844; 9.031 -> 9.293; 11.120 -> 11.243; 12.443 -> 12.670; 13.570 -> 13.776; 14.369 -> 14.497 | Helped |
| Use adaptive threshold rather than fixed threshold (ablation) | LTW · OPT-6.7B, watermark strengths δ = 1.5, 2, 2.5, 3, 3.5, and 4 | Perplexity: 11.801 -> 11.686; 12.524 -> 12.354; 13.217 -> 13.003; 13.403 -> 13.410; 13.922 -> 13.981; 14.308 -> 14.029 | Mixed |
Surprising findings
- The fixed green-list variant (LTW-0, Unigram-based) is more robust to paraphrasing than the hash-based LTW-1 variant, attributed to avoiding green-list changes caused by rewritten previous tokens.
- The adaptive threshold ablation shows only small differences in z-score and perplexity, with a lower perplexity in only 4 of 6 strength settings.
Limitations
- Experiments use only small models (OPT-1.3B/6.7B, GPT-J-6B) and a single dataset (C4 RealNewsLike).
- The selector is trained only on continuation generations from OPT-1.3B, so transfer to other generation tasks is untested.
- No error bars or statistical significance reported; a fixed random key was used.
Experimental setup
Datasets: C4 RealNewsLike
Benchmarks: C4 RealNewsLike test set (500 samples)
Metrics: AUROC Best F1 TPR@FPR perplexity sentence embedding similarity
Baselines: KGW Unigram EXP-edit SWEET TS-watermark
Builds on: KGW watermark Unigram watermark SWEET MGDA SimCSE
Closest papers by meaning
- Token-Specific Watermarking with Enhanced Detectability and Semantic Coherence for Large Language Models (ICML 2024 · similarity 0.92)
- Theoretically Grounded Framework for LLM Watermarking: A Distribution-Adaptive Approach (NeurIPS 2025 · similarity 0.92)
- PRO: Enabling Precise and Robust Text Watermark for Open-Source LLMs (NeurIPS 2026 · similarity 0.89)
- Adaptive Text Watermark for Large Language Models (ICML 2024 · similarity 0.89)
- On the Learnability of Watermarks for Language Models (ICLR 2024 · similarity 0.89)
- BiMark: Unbiased Multilayer Watermarking for Large Language Models (ICML 2025 · similarity 0.89)
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