David L. Donoho

Matthias Gerstgrasser, Rylan Schaeffer, Apratim Dey et al.

The proliferation of generative models, combined with pretraining on web-scale data, raises a timely question: what happens when these models are trained on their own generated outputs? Recent investigations into model-data feedback loops proposed that such loops would lead to a phenomenon termed model collapse, under which performance progressively degrades with each model-data feedback iteration until fitted models become useless. However, those studies largely assumed that new data replace old data over time, where an arguably more realistic assumption is that data accumulate over time. In this paper, we ask: what effect does accumulating data have on model collapse? We empirically study this question by pretraining sequences of language models on text corpora. We confirm that replacing the original real data by each generation's synthetic data does indeed tend towards model collapse, then demonstrate that accumulating the successive generations of synthetic data alongside the original real data avoids model collapse; these results hold across a range of model sizes, architectures, and hyperparameters. We obtain similar results for deep generative models on other types of real data: diffusion models for molecule conformation generation and variational autoencoders for image generation. To understand why accumulating data can avoid model collapse, we use an analytically tractable framework introduced by prior work in which a sequence of linear models are fit to the previous models' outputs. Previous work used this framework to show that if data are replaced, the test error increases with the number of model-fitting iterations; we extend this argument to prove that if data instead accumulate, the test error has a finite upper bound independent of the number of iterations, meaning model collapse no longer occurs.

Joshua Kazdan, Rylan Schaeffer, Apratim Dey et al.

What happens when generative machine learning models are pretrained on web-scale datasets containing data generated by earlier models? Some prior work warns of "model collapse" as the web is overwhelmed by synthetic data; other work suggests the problem can be contained (i.e. collapse can be avoided) by managing how available data are used in pretraining. In this paper, we report experiments on three ways of using data (training-workflows), across three generative model task-settings (multivariate Gaussian estimation, kernel density estimation, and language-model fine-tuning) to further confirm the possibility of containment: (a) we confirm that the training-workflow of {\it replacing} all real data by successive generations of purely synthetic data indeed suffers model collapse in all task-settings studied; (b) we consider the training-workflow of {\it accumulating} synthetic data alongside real data and training on all data combined and confirming that, although the proportion of real data eventually becomes zero, models remain stable and their test losses do not diverge under this training-workflow; (c) we consider a training-workflow where real and synthetic data accumulate together but successive generations of pretraining are constrained to use fixed-size data subsets each generation. In this workflow, we observe slow and gradual rather than explosive degradation of test loss performance across generations. Our insights are particularly important when forecasting whether future frontier generative models will collapse or thrive, and our results open avenues for empirically and mathematically studying the context-dependent value of synthetic data.