From Collapse to Improvement: Statistical Perspectives on the Evolutionary Dynamics of Iterative Training on Contaminated Sources

TL;DR

This paper offers a statistical analysis of iterative training on contaminated data, demonstrating conditions under which models can avoid collapse and improve by leveraging true data amidst synthetic contamination.

Contribution

It provides a novel statistical framework analyzing how iterative training on mixed data influences model evolution and performance, highlighting conditions for recovery of the true distribution.

Findings

Training with a non-trivial true data mixture can prevent collapse.

Proper sample sizes and mixture weights enable recovery of the true distribution.

Simulation results support the theoretical analysis across different models.

Abstract

The problem of model collapse has presented new challenges in iterative training of generative models, where such training with synthetic data leads to an overall degradation of performance. This paper looks at the problem from a statistical viewpoint, illustrating that one can actually hope for improvement when models are trained on data contaminated with synthetic samples, as long as there is some amount of fresh information from the true target distribution. In particular, we consider iterative training on samples sourced from a mixture of the true target and synthetic distributions. We analyze the entire iterative evolution in a next-token prediction language model, capturing how the interplay between the mixture weights and the sample size controls the overall long-term performance. With non-trivial mixture weight of the true distribution, even if it decays over time, simply training the model in a contamination-agnostic manner with appropriate sample sizes can avoid collapse and even recover the true target distribution under certain conditions. Simulation studies support our findings and also show that such behavior is more general for other classes of models.