# Inevitable Trade-off between Watermark Strength and Speculative Sampling Efficiency for Language Models arXiv: https://arxiv.org/abs/2410.20418 ยท HTML: https://mlsanity.com/paper/2410.20418/ ## Key facts - Cited by 8 papers in the map (data through 14 Oct 2026). - Placed in Speculative decoding, one of 12 directions in Efficient LLM inference and serving. - Builds on 36 of its 54 references that are in the map. - First posted on arXiv 27 Oct 2024. ## Placed in - Efficient LLM inference and serving / [Speculative decoding](https://mlsanity.com/inference/speculative-decoding/) - LLM safety and security / [Watermarking generated content and models](https://mlsanity.com/safety/watermarking-generated-content-and-models/) ## Builds on (most cited first, 30 of 36) - [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023) - [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021) - [Fast Inference from Transformers via Speculative Decoding](https://mlsanity.com/paper/2211.17192/) (2022) - [Get To The Point: Summarization with Pointer-Generator Networks](https://mlsanity.com/paper/1704.04368/) (2017) - [Teaching Machines to Read and Comprehend](https://mlsanity.com/paper/1506.03340/) (2015) - [Accelerating Large Language Model Decoding with Speculative Sampling](https://mlsanity.com/paper/2302.01318/) (2023) - [Medusa: Simple LLM Inference Acceleration Framework with Multiple Decoding Heads](https://mlsanity.com/paper/2401.10774/) (2024) - [A Watermark for Large Language Models](https://mlsanity.com/paper/2301.10226/) (2023) - [EAGLE: Speculative Sampling Requires Rethinking Feature Uncertainty](https://mlsanity.com/paper/2401.15077/) (2024) - [Robust Distortion-free Watermarks for Language Models](https://mlsanity.com/paper/2307.15593/) (2023) - [Provable Robust Watermarking for AI-Generated Text](https://mlsanity.com/paper/2306.17439/) (2023) - [Undetectable Watermarks for Language Models](https://mlsanity.com/paper/2306.09194/) (2023) - [On the Reliability of Watermarks for Large Language Models](https://mlsanity.com/paper/2306.04634/) (2023) - [DistillSpec: Improving Speculative Decoding via Knowledge Distillation](https://mlsanity.com/paper/2310.08461/) (2023) - [Accelerating LLM Inference with Staged Speculative Decoding](https://mlsanity.com/paper/2308.04623/) (2023) - [REST: Retrieval-Based Speculative Decoding](https://mlsanity.com/paper/2311.08252/) (2023) - [Pretrained Language Models for Text Generation: A Survey](https://mlsanity.com/paper/2201.05273/) (2022) - [A Semantic Invariant Robust Watermark for Large Language Models](https://mlsanity.com/paper/2310.06356/) (2023) - [Unbiased Watermark for Large Language Models](https://mlsanity.com/paper/2310.10669/) (2023) - [TriForce: Lossless Acceleration of Long Sequence Generation with Hierarchical Speculative Decoding](https://mlsanity.com/paper/2404.11912/) (2024) - [Three Bricks to Consolidate Watermarks for Large Language Models](https://mlsanity.com/paper/2308.00113/) (2023) - [Robust Multi-bit Natural Language Watermarking through Invariant Features](https://mlsanity.com/paper/2305.01904/) (2023) - [A Robust Semantics-based Watermark for Large Language Model against Paraphrasing](https://mlsanity.com/paper/2311.08721/) (2023) - [Watermarking Text Generated by Black-Box Language Models](https://mlsanity.com/paper/2305.08883/) (2023) - [Adaptive Text Watermark for Large Language Models](https://mlsanity.com/paper/2401.13927/) (2024) - [Inference with Reference: Lossless Acceleration of Large Language Models](https://mlsanity.com/paper/2304.04487/) (2023) - [A Statistical Framework of Watermarks for Large Language Models: Pivot, Detection Efficiency and Optimal Rules](https://mlsanity.com/paper/2404.01245/) (2024) - [PaSS: Parallel Speculative Sampling](https://mlsanity.com/paper/2311.13581/) (2023) - [CoProtector: Protect Open-Source Code against Unauthorized Training Usage with Data Poisoning](https://mlsanity.com/paper/2110.12925/) (2021) - [Tracing Text Provenance via Context-Aware Lexical Substitution](https://mlsanity.com/paper/2112.07873/) (2021) ## Built on by (most cited first, 8 of 8) - [MorphMark: Flexible Adaptive Watermarking for Large Language Models](https://mlsanity.com/paper/2505.11541/) (2025) - [Marking Code Without Breaking It: Code Watermarking for Detecting LLM-Generated Code](https://mlsanity.com/paper/2502.18851/) (2025) - [WaterMod: Modular Token-Rank Partitioning for Probability-Balanced LLM Watermarking](https://mlsanity.com/paper/2511.07863/) (2025) - [Do Large Language Models (Really) Need Statistical Foundations?](https://mlsanity.com/paper/2505.19145/) (2025) - [Visual Watermarking in the Era of Diffusion Models: Advances and Challenges](https://mlsanity.com/paper/2505.08197/) (2025) - [Improving the Trade-off Between Watermark Strength and Speculative Sampling Efficiency for Language Models](https://mlsanity.com/paper/2602.01428/) (2026) - [CODE ACROSTIC: Robust Watermarking for Code Generation](https://mlsanity.com/paper/2512.14753/) (2025) - [Watermarkable Multi-Draft Speculative Sampling via Poisson Processes](https://mlsanity.com/paper/2609.21858/) (2026) ## Abstract (arXiv) Large language models are probabilistic models, and the process of generating content is essentially sampling from the output distribution of the language model. Existing watermarking techniques inject watermarks into the generated content without altering the output quality. On the other hand, existing acceleration techniques, specifically speculative sampling, leverage a draft model to speed up the sampling process while preserving the output distribution. However, there is no known method to simultaneously accelerate the sampling process and inject watermarks into the generated content. In this paper, we investigate this direction and find that the integration of watermarking and acceleration is non-trivial. We prove a no-go theorem, which states that it is impossible to simultaneously maintain the highest watermark strength and the highest sampling efficiency. Furthermore, we propose two methods that maintain either the sampling efficiency or the watermark strength, but not both. Our work provides a rigorous theoretical foundation for understanding the inherent trade-off between watermark strength and sampling efficiency in accelerating the generation of watermarked tokens for large language models. We also conduct numerical experiments to validate our theoretical findings and demonstrate the effectiveness of the proposed methods.