Data Compressibility Quantifies LLM Memorization

TL;DR

This paper introduces a set-level entropy-based metric to reliably quantify LLM memorization, revealing a linear relationship between data entropy and memorization scores.

Contribution

It uncovers the Entropy–Memorization Linearity, a robust phenomenon linking data entropy to memorization in large language models, improving quantitative analysis.

Findings

Set-level entropy correlates linearly with memorization scores.

Prior instance-level metrics failed to reliably quantify memorization.

The proposed approach offers a robust, quantitative measure of LLM memorization.

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.