# Data-Copying in Generative Models: A Formal Framework

arXiv: https://arxiv.org/abs/2302.13181 · HTML: https://mlsanity.com/paper/2302.13181/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 21 references that are in the map.
- First posted on arXiv 25 Feb 2023.

## Builds on (most cited first, 13 of 13)

- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [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)
- [Does Learning Require Memorization? A Short Tale about a Long Tail](https://mlsanity.com/paper/1906.05271/) (2019)
- [Assessing Generative Models via Precision and Recall](https://mlsanity.com/paper/1806.00035/) (2018)
- [Revisiting Classifier Two-Sample Tests](https://mlsanity.com/paper/1610.06545/) (2016)
- [When is Memorization of Irrelevant Training Data Necessary for High-Accuracy Learning?](https://mlsanity.com/paper/2012.06421/) (2020)
- [An empirical study on evaluation metrics of generative adversarial networks](https://mlsanity.com/paper/1806.07755/) (2018)
- [On GANs and GMMs](https://mlsanity.com/paper/1805.12462/) (2018)
- [On Memorization in Probabilistic Deep Generative Models](https://mlsanity.com/paper/2106.03216/) (2021)
- [Intrinsic Dimension Estimation Using Wasserstein Distances](https://mlsanity.com/paper/2106.04018/) (2021)
- [On Training Sample Memorization: Lessons from Benchmarking Generative Modeling with a Large-scale Competition](https://mlsanity.com/paper/2106.03062/) (2021)
- [Empirical Analysis of Overfitting and Mode Drop in GAN Training](https://mlsanity.com/paper/2006.14265/) (2020)

## Built on by (most cited first, 9 of 9)

- [How much do language models memorize?](https://mlsanity.com/paper/2505.24832/) (2025)
- [A Geometric Framework for Understanding Memorization in Generative Models](https://mlsanity.com/paper/2411.00113/) (2024)
- [Understanding and Mitigating Memorization in Generative Models via Sharpness of Probability Landscapes](https://mlsanity.com/paper/2412.04140/) (2024)
- [Data Plagiarism Index: Characterizing the Privacy Risk of Data-Copying in Tabular Generative Models](https://mlsanity.com/paper/2406.13012/) (2024)
- [Advancing Retail Data Science: Comprehensive Evaluation of Synthetic Data](https://mlsanity.com/paper/2406.13130/) (2024)
- [On Convolutions, Intrinsic Dimension, and Diffusion Models](https://mlsanity.com/paper/2506.20705/) (2025)
- [Local Lesion Generation is Effective for Capsule Endoscopy Image Data Augmentation in a Limited Data Setting](https://mlsanity.com/paper/2411.03098/) (2024)
- [Generation Properties of Stochastic Interpolation under Finite Training Set](https://mlsanity.com/paper/2509.21925/) (2025)
- [The Null Is the Hard Part: Exact Tests for Memorization in Generative Models](https://mlsanity.com/paper/2610.00251/) (2026)

## Abstract (arXiv)

There has been some recent interest in detecting and addressing memorization of training data by deep neural networks. A formal framework for memorization in generative models, called "data-copying," was proposed by Meehan et. al. (2020). We build upon their work to show that their framework may fail to detect certain kinds of blatant memorization. Motivated by this and the theory of non-parametric methods, we provide an alternative definition of data-copying that applies more locally. We provide a method to detect data-copying, and provably show that it works with high probability when enough data is available. We also provide lower bounds that characterize the sample requirement for reliable detection.