# Improving the Trade-off Between Watermark Strength and Speculative Sampling Efficiency for Language Models

arXiv: https://arxiv.org/abs/2602.01428 · HTML: https://mlsanity.com/paper/2602.01428/

## Key facts

- Cited by 1 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 42 of its 54 references that are in the map.
- First posted on arXiv 1 Feb 2026.

## 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 42)

- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Fast Inference from Transformers via Speculative Decoding](https://mlsanity.com/paper/2211.17192/) (2022)
- [Accelerating Large Language Model Decoding with Speculative Sampling](https://mlsanity.com/paper/2302.01318/) (2023)
- [Gemma: Open Models Based on Gemini Research and Technology](https://mlsanity.com/paper/2403.08295/) (2024)
- [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)
- [ELI5: Long Form Question Answering](https://mlsanity.com/paper/1907.09190/) (2019)
- [Can AI-Generated Text be Reliably Detected?](https://mlsanity.com/paper/2303.11156/) (2023)
- [SpecInfer: Accelerating Generative Large Language Model Serving with Tree-based Speculative Inference and Verification](https://mlsanity.com/paper/2305.09781/) (2023)
- [Blockwise Parallel Decoding for Deep Autoregressive Models](https://mlsanity.com/paper/1811.03115/) (2018)
- [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)
- [Unlocking Efficiency in Large Language Model Inference: A Comprehensive Survey of Speculative Decoding](https://mlsanity.com/paper/2401.07851/) (2024)
- [On the Reliability of Watermarks for Large Language Models](https://mlsanity.com/paper/2306.04634/) (2023)
- [Speculative Decoding: Exploiting Speculative Execution for Accelerating Seq2seq Generation](https://mlsanity.com/paper/2203.16487/) (2022)
- [DistillSpec: Improving Speculative Decoding via Knowledge Distillation](https://mlsanity.com/paper/2310.08461/) (2023)
- [Speculative Decoding with Big Little Decoder](https://mlsanity.com/paper/2302.07863/) (2023)
- [A* Sampling](https://mlsanity.com/paper/1411.0030/) (2014)
- [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)
- [SpecTr: Fast Speculative Decoding via Optimal Transport](https://mlsanity.com/paper/2310.15141/) (2023)
- [Online Speculative Decoding](https://mlsanity.com/paper/2310.07177/) (2023)
- [Unbiased Watermark for Large Language Models](https://mlsanity.com/paper/2310.10669/) (2023)
- [Three Bricks to Consolidate Watermarks for Large Language Models](https://mlsanity.com/paper/2308.00113/) (2023)
- [Adaptive Text Watermark for Large Language Models](https://mlsanity.com/paper/2401.13927/) (2024)
- [A Statistical Framework of Watermarks for Large Language Models: Pivot, Detection Efficiency and Optimal Rules](https://mlsanity.com/paper/2404.01245/) (2024)
- [A Resilient and Accessible Distribution-Preserving Watermark for Large Language Models](https://mlsanity.com/paper/2310.07710/) (2023)

## Built on by (most cited first, 1 of 1)

- [Watermarkable Multi-Draft Speculative Sampling via Poisson Processes](https://mlsanity.com/paper/2609.21858/) (2026)

## Abstract (arXiv)

Watermarking is a principled approach for tracing the provenance of large language model (LLM) outputs, but its deployment in practice is hindered by inference inefficiency. Speculative sampling accelerates inference, with efficiency improving as the acceptance rate between draft and target models increases. Yet recent work reveals a fundamental trade-off: higher watermark strength reduces acceptance, preventing their simultaneous achievement. We revisit this trade-off and show it is not absolute. We introduce a quantitative measure of watermark strength that governs statistical detectability and is maximized when tokens are deterministic functions of pseudorandom numbers. Using this measure, we fully characterize the trade-off as a constrained optimization problem and derive explicit Pareto curves for two existing watermarking schemes. Finally, we introduce a principled mechanism that injects pseudorandomness into draft-token acceptance, ensuring maximal watermark strength while maintaining speculative sampling efficiency. Experiments further show that this approach improves detectability without sacrificing efficiency. Our findings uncover a principle that unites speculative sampling and watermarking, paving the way for their efficient and practical deployment.