# Linear Ensembles Wash Away Watermarks: On the Fragility of Distributional Perturbations in LLMs

arXiv: https://arxiv.org/abs/2605.30501 · HTML: https://mlsanity.com/paper/2605.30501/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Watermarking generated content and models, one of 12 directions in LLM safety and security.
- Builds on 26 of its 33 references that are in the map.
- First posted on arXiv 28 May 2026.

## Placed in

- LLM safety and security / [Watermarking generated content and models](https://mlsanity.com/safety/watermarking-generated-content-and-models/)

## Builds on (most cited first, 26 of 26)

- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [A Survey on Large Language Model based Autonomous Agents](https://mlsanity.com/paper/2308.11432/) (2023)
- [Jailbroken: How Does LLM Safety Training Fail?](https://mlsanity.com/paper/2307.02483/) (2023)
- [A Watermark for Large Language Models](https://mlsanity.com/paper/2301.10226/) (2023)
- [Paraphrasing evades detectors of AI-generated text, but retrieval is an effective defense](https://mlsanity.com/paper/2303.13408/) (2023)
- [A Survey on Large Language Model (LLM) Security and Privacy: The Good, the Bad, and the Ugly](https://mlsanity.com/paper/2312.02003/) (2023)
- [Robust Distortion-free Watermarks for Language Models](https://mlsanity.com/paper/2307.15593/) (2023)
- [On the Reliability of Watermarks for Large Language Models](https://mlsanity.com/paper/2306.04634/) (2023)
- [Large Language Models for Education: A Survey and Outlook](https://mlsanity.com/paper/2403.18105/) (2024)
- [A Survey of Text Watermarking in the Era of Large Language Models](https://mlsanity.com/paper/2312.07913/) (2023)
- [Unbiased Watermark for Large Language Models](https://mlsanity.com/paper/2310.10669/) (2023)
- [WritingBench: A Comprehensive Benchmark for Generative Writing](https://mlsanity.com/paper/2503.05244/) (2025)
- [MarkLLM: An Open-Source Toolkit for LLM Watermarking](https://mlsanity.com/paper/2405.10051/) (2024)
- [Watermark Stealing in Large Language Models](https://mlsanity.com/paper/2402.19361/) (2024)
- [Watermarks in the Sand: Impossibility of Strong Watermarking for Generative Models](https://mlsanity.com/paper/2311.04378/) (2023)
- [Harnessing Multiple Large Language Models: A Survey on LLM Ensemble](https://mlsanity.com/paper/2502.18036/) (2025)
- [A Resilient and Accessible Distribution-Preserving Watermark for Large Language Models](https://mlsanity.com/paper/2310.07710/) (2023)
- [No Free Lunch in LLM Watermarking: Trade-offs in Watermarking Design Choices](https://mlsanity.com/paper/2402.16187/) (2024)
- [Breaking the Ceiling of the LLM Community by Treating Token Generation as a Classification for Ensembling](https://mlsanity.com/paper/2406.12585/) (2024)
- [Bypassing LLM Watermarks with Color-Aware Substitutions](https://mlsanity.com/paper/2403.14719/) (2024)
- [Debiasing Watermarks for Large Language Models via Maximal Coupling](https://mlsanity.com/paper/2411.11203/) (2024)
- [Can Watermarked LLMs be Identified by Users via Crafted Prompts?](https://mlsanity.com/paper/2410.03168/) (2024)
- [Watermarking Low-entropy Generation for Large Language Models: An Unbiased and Low-risk Method](https://mlsanity.com/paper/2405.14604/) (2024)

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

- [Pin It on Anyone: Certified Targeted Displacement of Multi-Bit LLM Watermarks Without the Key](https://mlsanity.com/paper/2610.18359/) (2026)

## Abstract (arXiv)

Watermarking embeds statistical signatures in AI-generated text for detection and attribution. We reveal a fundamental vulnerability: when users access multiple models (today's reality), watermarks trivially fail. Watermarks perturb output distributions away from the original, and in competitive markets, these perturbations are typically independent across providers. We theoretically prove that averaging output probability distributions recovers the unwatermarked distribution with up to a second-order error term. Empirically, simply averaging 3-5 models cancels out these perturbations. We introduce WASH (Watermark Attenuation via Statistical Hybridisation), which solves practical challenges in ensemble generation: vocabulary misalignment and tokenisation differences across heterogeneous models. Experiments across six watermarking schemes and three LLMs show that averaging across 3 models suppresses detection z-scores from 5-300 to below 2 (below the detection threshold of 4) and reduces TPR at 5% FPR to below 50%, while improving quality by 27.5% and running 6 times faster than the best baseline on the long sequence generation. Our results suggest that robust AI-text detection via watermarking requires either accepting this fundamental vulnerability or unprecedented coordination among model providers.