Data Compressibility Quantifies LLM Memorization

Large Language Models (LLMs) are known to memorize portions of their training data, sometimes even reproduce content verbatim when prompted appropriately. Despite substantial interest, existing LLM memorization research has offered limited insight into how training data influences memorization and largely lacks quantitative characterization. In this work, we build upon the line of research that seeks to quantify memorization through data compressibility. We analyze why prior attempts fail to yield a reliable quantitative measure and show that a surprisingly simple shift from instance-level to set-level metrics uncovers a robust phenomenon, which we term the \textit{Entropy--Memorization (EM) Linearity}. This law states that a set-level data entropy estimator exhibits a linear correlation with memorization scores. We validate the EM Linearity through extensive experiments across a wide range of open-source models and experimental configurations. We further investigate the role of the token space—an implicit yet pivotal factor in our method—and identify an additional variant of the EM Law. Besides, we made a side observation that EM Linearity enables a simple application to distinguish between LLM train data and test data.

Authors

• Yizhan Huang The Chinese University of Hong Kong
• Zhe Yang Peking University
• Meifang Chen
• HUANG Nianchen
• Jianping Zhang The Chinese University of Hong Kong
• Michael R. Lyu The Chinese University of Hong Kong

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