# SSG: Logit-Balanced Vocabulary Partitioning for LLM Watermarking

arXiv: https://arxiv.org/abs/2604.22438 · HTML: https://mlsanity.com/paper/2604.22438/

## Key facts

- Cited by 2 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 18 of its 24 references that are in the map.
- First posted on arXiv 24 Apr 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, 18 of 18)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Teaching Machines to Read and Comprehend](https://mlsanity.com/paper/1506.03340/) (2015)
- [Robust Distortion-free Watermarks for Language Models](https://mlsanity.com/paper/2307.15593/) (2023)
- [Who Wrote this Code? Watermarking for Code Generation](https://mlsanity.com/paper/2305.15060/) (2023)
- [A Survey of Text Watermarking in the Era of Large Language Models](https://mlsanity.com/paper/2312.07913/) (2023)
- [MarkLLM: An Open-Source Toolkit for LLM Watermarking](https://mlsanity.com/paper/2405.10051/) (2024)
- [On the Learnability of Watermarks for Language Models](https://mlsanity.com/paper/2312.04469/) (2023)
- [An Entropy-based Text Watermarking Detection Method](https://mlsanity.com/paper/2403.13485/) (2024)
- [CoProtector: Protect Open-Source Code against Unauthorized Training Usage with Data Poisoning](https://mlsanity.com/paper/2110.12925/) (2021)
- [CodeMark: Imperceptible Watermarking for Code Datasets against Neural Code Completion Models](https://mlsanity.com/paper/2308.14401/) (2023)
- [WatME: Towards Lossless Watermarking Through Lexical Redundancy](https://mlsanity.com/paper/2311.09832/) (2023)
- [WaterMod: Modular Token-Rank Partitioning for Probability-Balanced LLM Watermarking](https://mlsanity.com/paper/2511.07863/) (2025)

## Built on by (most cited first, 2 of 2)

- [RMCW: A Deletion-Robust Watermark Based on Reed--Muller Codes for Language Models](https://mlsanity.com/paper/2610.02817/) (2026)
- [Language Model Fingerprinting Requires Rethinking Watermark Teachers](https://mlsanity.com/paper/2610.04169/) (2026)

## Abstract (arXiv)

Watermarking has emerged as a promising technique for tracing the authorship of content generated by large language models (LLMs). Among existing approaches, the KGW scheme is particularly attractive due to its versatility, efficiency, and effectiveness in natural language generation. However, KGW's effectiveness degrades significantly under low-entropy settings such as code generation and mathematical reasoning. A crucial step in the KGW method is random vocabulary partitioning, which enables adjustments to token selection based on specific preferences. Our study revealed that the next-token probability distribution plays an critical role in determining how much, or even whether, we can modify token selection and, consequently, the effectiveness of watermarking. We refer to this characteristic, associated with the probability distribution of each token prediction, as watermark strength. In cases of random vocabulary partitioning, the lower bound of watermark strength is dictated by the next-token probability distribution. However, we found that, by redesigning the vocabulary partitioning algorithm, we can potentially raise this lower bound. In this paper, we propose SSG (Sort-then-Split by Groups), a method that partitions the vocabulary into two logit-balanced subsets. This design lifts the lower bound of watermark strength for each token prediction, thereby improving watermark detectability. Experiments on code generation and mathematical reasoning datasets demonstrate the effectiveness of SSG.