Rate of Model Collapse in Recursive Training

TL;DR

This paper investigates how quickly models trained recursively on generated data tend to forget original data nuances, providing theoretical and experimental insights into the rate of model collapse for fundamental distributions.

Contribution

It offers the first theoretical characterization of the rate of model collapse in recursive training for discrete and Gaussian distributions under maximum likelihood estimation.

Findings

For discrete distributions, the time to forget a word is roughly proportional to its original frequency.

For Gaussian models, the standard deviation diminishes to zero after approximately n iterations.

Model forgetting takes a long time in these simple distribution settings.

Abstract

Given the ease of creating synthetic data from machine learning models, new models can be potentially trained on synthetic data generated by previous models. This recursive training process raises concerns about the long-term impact on model quality. As models are recursively trained on generated data from previous rounds, their ability to capture the nuances of the original human-generated data may degrade. This is often referred to as \emph{model collapse}. In this work, we ask how fast model collapse occurs for some well-studied distribution families under maximum likelihood (ML or near ML) estimation during recursive training. Surprisingly, even for fundamental distributions such as discrete and Gaussian distributions, the exact rate of model collapse is unknown. In this work, we theoretically characterize the rate of collapse in these fundamental settings and complement it with experimental evaluations. Our results show that for discrete distributions, the time to forget a word is approximately linearly dependent on the number of times it occurred in the original corpus, and for Gaussian models, the standard deviation reduces to zero roughly at $n$ iterations, where $n$ is the number of samples at each iteration. Both of these findings imply that model forgetting, at least in these simple distributions under near ML estimation with many samples, takes a long time.