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Life sciences · Preprint
arXiv · September 3, 2026
Early or partial results. Treat as a signal, not a conclusion.
This preprint introduces Stateless Bernoulli Watermarking, a proposed method to embed statistical watermarks in LLM outputs with reduced computational complexity and claimed equivalence to existing methods. The work is a computational optimization paper with theoretical guarantees and benchmark data, but has not undergone peer review and does not evaluate robustness to adversarial detection or removal attempts.
Computational methods paper with theoretical proofs and benchmarking. Large Language Models (models and datasets not specified by name or count in source text). Intervention: Stateless Bernoulli Watermarking (SBW) using independent per-token Bernoulli trials with counter-based random number generation and GPU-native Jenkins hash function. Compared with: KGW (vocabulary permutation) and SynthID (multi-layer tournament) watermarking methods.
SBW membership complexity is O(1) with single-kernel execution and zero intermediate allocations, compared to permutation and tournament methods used by KGW and SynthID Full-vocabulary self-salt watermarking speed is over 6000× faster than KGW and 2× faster than SynthID End-to-end generation overhead is less than 1% across all batch sizes
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The source did not state who this applies to in practice.
This is a preprint describing a novel computational method for LLM watermarking with theoretical proofs and benchmark results, but lacks peer review, clinical validation, or real-world deployment evidence needed for practice-changing claims.
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We introduce Stateless Bernoulli Watermarking (SBW), a new statistical watermark for Large Language Models that determines green list membership through independent per-token Bernoulli trials. Unlike KGW's vocabulary permutation or SynthID's multi-layer tournament, SBW requires only a single comparison per token against a counter-based random number generator, reducing membership complexity to $O(1)$ and enabling single-kernel execution with zero intermediate allocations. We prove that this formulation preserves the same detection guarantees as fixed-size green lists: the z-score test remains $\mathcal{N}(0,1)$ under the null. The stateless architecture enables capabilities unavailable to existing methods: full-vocabulary self-salt watermarking (over 6000$\times$ faster than KGW's self-salt and 2$\times$ faster than SynthID despite biasing the entire vocabulary with candidate-dependent seeding) and architectural compatibility with distributed inference. In end-to-end generation benchmarks, SBW adds less than 1\% overhead at all batch sizes. We additionally identify hash function design as a previously unexplored axis for watermark quality, showing that a GPU-native Jenkins hash improves null calibration by 1.8$\times$ while producing more diverse text. Experiments across two seeding schemes and eight $(γ, δ)$ configurations confirm statistical equivalence with ROC-AUC differences below 0.01.
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