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Diffusion models are powerful generative models that produce high-quality samples from complex data. While their infinite-data behavior is well understood, their generalization with finite data remains less clear. Classical learning theory…

Machine Learning · Statistics 2026-02-02 Claudia Merger , Sebastian Goldt

Diffusion models generate high-quality samples but can also memorize training data, raising serious privacy concerns. Understanding the mechanisms governing when memorization versus generalization occurs remains an active area of research.…

Machine Learning · Computer Science 2026-02-23 Nick Dodson , Xinyu Gao , Qingsong Wang , Yusu Wang , Zhengchao Wan

The success of modern neural networks has prompted study of the connection between memorisation and generalisation: overparameterised models generalise well, despite being able to perfectly fit (memorise) completely random labels. To…

Machine Learning · Computer Science 2023-10-10 Michal Lukasik , Vaishnavh Nagarajan , Ankit Singh Rawat , Aditya Krishna Menon , Sanjiv Kumar

The relationship between memorization and generalization in large language models (LLMs) remains an open area of research, with growing evidence that the two are deeply intertwined. In this work, we investigate this relationship by…

Machine Learning · Computer Science 2025-06-19 Joshua Barron , Devin White

Machine learning models exhibit two seemingly contradictory phenomena: training data memorization, and various forms of forgetting. In memorization, models overfit specific training examples and become susceptible to privacy attacks. In…

Reasoning is an integral part of many tasks performed by language models (LMs). However, the effects of scaling model sizes and data on reasoning abilities at pretraining time remain understudied. To rigorously investigate this problem, we…

Artificial Intelligence · Computer Science 2025-09-30 Xinyi Wang , Shawn Tan , Shenbo Xu , Mingyu Jin , William Yang Wang , Rameswar Panda , Yikang Shen

We examine the connection between training error and generalization error for arbitrary estimating procedures, working in an overparameterized linear model under general priors in a Bayesian setup. We find determining factors inherent to…

Machine Learning · Statistics 2026-02-11 Chen Cheng , Rina Foygel Barber

Generative neural networks learn how to produce highly realistic images from a large, but finite number of examples - or do they simply memorise their training set? To settle this question, Kadkhodaie, Guth, Simoncelli and Mallat (ICLR '24)…

Machine Learning · Statistics 2026-05-21 Antoine Maillard , Sebastian Goldt

One of the objectives of Continual Learning is to learn new concepts continually over a stream of experiences and at the same time avoid catastrophic forgetting. To mitigate complete knowledge overwriting, memory-based methods store a…

Machine Learning · Computer Science 2023-06-21 Felipe del Rio , Julio Hurtado , Cristian Buc , Alvaro Soto , Vincenzo Lomonaco

There is strong empirical evidence that the state-of-the-art diffusion modeling paradigm leads to models that memorize the training set, especially when the training set is small. Prior methods to mitigate the memorization problem often…

Machine Learning · Computer Science 2026-03-03 Kulin Shah , Alkis Kalavasis , Adam R. Klivans , Giannis Daras

Large Language Models (LLMs), trained on massive corpora with billions of parameters, show unprecedented performance in various fields. Though surprised by their excellent performances, researchers also noticed some special behaviors of…

Computation and Language · Computer Science 2024-06-05 Bowen Chen , Namgi Han , Yusuke Miyao

The impressive capabilities of large language models (LLMs) have sparked debate over whether these models genuinely generalize to unseen tasks or predominantly rely on memorizing vast amounts of pretraining data. To explore this issue, we…

Computation and Language · Computer Science 2025-03-04 Xinyi Wang , Antonis Antoniades , Yanai Elazar , Alfonso Amayuelas , Alon Albalak , Kexun Zhang , William Yang Wang

The modeling of probability distributions, specifically generative modeling and density estimation, has become an immensely popular subject in recent years by virtue of its outstanding performance on sophisticated data such as images and…

Machine Learning · Statistics 2023-01-02 Hongkang Yang

Diffusion models power leading generative AI, but when and how they memorize training data, especially on low-dimensional manifolds, remains unclear. We find memorization emerges gradually, not abruptly: as data become scarce, diffusion…

The diffusion probabilistic generative models are widely used to generate high-quality data. Though they can synthetic data that does not exist in the training set, the rationale behind such generalization is still unexplored. In this…

Machine Learning · Computer Science 2023-05-25 Mingyang Yi , Jiacheng Sun , Zhenguo Li

Memorisation is a natural part of learning from real-world data: neural models pick up on atypical input-output combinations and store those training examples in their parameter space. That this happens is well-known, but how and where are…

Computation and Language · Computer Science 2024-08-12 Verna Dankers , Ivan Titov

AI models present a wide range of applications in the field of medicine. However, achieving optimal performance requires access to extensive healthcare data, which is often not readily available. Furthermore, the imperative to preserve…

Natural data is often organized as a hierarchical composition of features. How many samples do generative models need in order to learn the composition rules, so as to produce a combinatorially large number of novel data? What signal in the…

Machine Learning · Statistics 2025-06-05 Alessandro Favero , Antonio Sclocchi , Francesco Cagnetta , Pascal Frossard , Matthieu Wyart

Controlling memorization in diffusion models is critical for applications that require generated data to closely match the training distribution. Existing approaches mainly focus on data centric or model centric modifications, treating the…

Machine Learning · Computer Science 2026-01-30 Thuy Phuong Vu , Mai Viet Hoang Do , Minhhuy Le , Dinh-Cuong Hoang , Phan Xuan Tan

In this paper we propose to study generalization of neural networks on small algorithmically generated datasets. In this setting, questions about data efficiency, memorization, generalization, and speed of learning can be studied in great…

Machine Learning · Computer Science 2022-01-07 Alethea Power , Yuri Burda , Harri Edwards , Igor Babuschkin , Vedant Misra