# A Geometric Framework for Understanding Memorization in Generative Models

Source: [A Geometric Framework for Understanding Memorization in Generative Models](<https://www.sota2.com/research/paper/68fa77691e209131cea7321c>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-26T04:18:49.615Z

Authors: Brendan Leigh Ross, Hamidreza Kamkari, Tongzi Wu, Rasa Hosseinzadeh, Zhaoyan Liu, George Stein, Jesse C. Cresswell, Gabriel Loaiza-Ganem

Published: 2024-10-31T18:09:01.000Z

## Abstract

As deep generative models have progressed, recent work has shown them to be capable of memorizing and reproducing training datapoints when deployed. These findings call into question the usability of generative models, especially in light of the legal and privacy risks brought about by memorization. To better understand this phenomenon, we propose the manifold memorization hypothesis (MMH), a geometric framework which leverages the manifold hypothesis into a clear language in which to reason about memorization. We propose to analyze memorization in terms of the relationship between the dimensionalities of (i) the ground truth data manifold and (ii) the manifold learned by the model. This framework provides a formal standard for "how memorized" a datapoint is and systematically categorizes memorized data into two types: memorization driven by overfitting and memorization driven by the underlying data distribution. By analyzing prior work in the context of the MMH, we explain and unify assorted observations in the literature. We empirically validate the MMH using synthetic data and image datasets up to the scale of Stable Diffusion, developing new tools for detecting and preventing generation of memorized samples in the process.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Memorization Detection on ImageNet-DiT](<https://www.sota2.com/research/sota/memorization-detection-on-imagenet-dit.md>): Memorization Detection; ImageNet-DiT; AUC: 97.1.

- [Memorization Detection on CIFAR10 EDM](<https://www.sota2.com/research/sota/memorization-detection-on-cifar10-edm.md>): Memorization Detection; CIFAR10 EDM; AUC: 71.3.

- [Memorization Detection on Stable Diffusion v1.4](<https://www.sota2.com/research/sota/memorization-detection-on-stable-diffusion-v1-4.md>): Memorization Detection; Stable Diffusion V1.4; AUC: 0.956.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2411.00113>)

[PDF](<https://arxiv.org/pdf/2411.00113.pdf>)