Data Compressibility Quantifies LLM Memorization

arXiv:2507.06056v4 Announce Type: replace Abstract: 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.