# Data Compressibility Quantifies LLM Memorization

arXiv: https://arxiv.org/abs/2507.06056 · HTML: https://mlsanity.com/paper/2507.06056/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 61 references that are in the map.
- First posted on arXiv 8 Jul 2025.

## Builds on (most cited first, 30 of 43)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [Extracting Training Data from Large Language Models](https://mlsanity.com/paper/2012.07805/) (2020)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [Membership Inference Attacks From First Principles](https://mlsanity.com/paper/2112.03570/) (2021)
- [The Secret Sharer: Evaluating and Testing Unintended Memorization in Neural Networks](https://mlsanity.com/paper/1802.08232/) (2018)
- [Quantifying Memorization Across Neural Language Models](https://mlsanity.com/paper/2202.07646/) (2022)
- [SFT Memorizes, RL Generalizes: A Comparative Study of Foundation Model Post-training](https://mlsanity.com/paper/2501.17161/) (2025)
- [OLMo: Accelerating the Science of Language Models](https://mlsanity.com/paper/2402.00838/) (2024)
- [What Neural Networks Memorize and Why: Discovering the Long Tail via Influence Estimation](https://mlsanity.com/paper/2008.03703/) (2020)
- [Dolma: an Open Corpus of Three Trillion Tokens for Language Model Pretraining Research](https://mlsanity.com/paper/2402.00159/) (2024)
- [Does Learning Require Memorization? A Short Tale about a Long Tail](https://mlsanity.com/paper/1906.05271/) (2019)
- [2 OLMo 2 Furious](https://mlsanity.com/paper/2501.00656/) (2024)
- [Deduplicating Training Data Mitigates Privacy Risks in Language Models](https://mlsanity.com/paper/2202.06539/) (2022)
- [LiveBench: A Challenging, Contamination-Limited LLM Benchmark](https://mlsanity.com/paper/2406.19314/) (2024)
- [Membership Inference Attacks against Language Models via Neighbourhood Comparison](https://mlsanity.com/paper/2305.18462/) (2023)
- [Memorization Without Overfitting: Analyzing the Training Dynamics of Large Language Models](https://mlsanity.com/paper/2205.10770/) (2022)
- [Do Membership Inference Attacks Work on Large Language Models?](https://mlsanity.com/paper/2402.07841/) (2024)
- [Counterfactual Memorization in Neural Language Models](https://mlsanity.com/paper/2112.12938/) (2021)
- [Emergent and Predictable Memorization in Large Language Models](https://mlsanity.com/paper/2304.11158/) (2023)
- [ProPILE: Probing Privacy Leakage in Large Language Models](https://mlsanity.com/paper/2307.01881/) (2023)
- [How much do language models copy from their training data? Evaluating linguistic novelty in text generation using RAVEN](https://mlsanity.com/paper/2111.09509/) (2021)
- [Generalization or Memorization: Data Contamination and Trustworthy Evaluation for Large Language Models](https://mlsanity.com/paper/2402.15938/) (2024)
- [Dataset Inference: Ownership Resolution in Machine Learning](https://mlsanity.com/paper/2104.10706/) (2021)
- [LLM Dataset Inference: Did you train on my dataset?](https://mlsanity.com/paper/2406.06443/) (2024)
- [Preventing Verbatim Memorization in Language Models Gives a False Sense of Privacy](https://mlsanity.com/paper/2210.17546/) (2022)
- [Rethinking LLM Memorization through the Lens of Adversarial Compression](https://mlsanity.com/paper/2404.15146/) (2024)

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

- [Extracting alignment data in open models](https://mlsanity.com/paper/2510.18554/) (2025)

## Abstract (arXiv)

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 textitEntropy--Memorization (EM) Linearity. This law states that a set-level data entropy estimator exhibits a linear correlation with memorization scores.