Statistical Analysis of Synthetic Data with Verification: A Linear Regression Framework

arXiv:2610.40254v1 Announce Type: new Abstract: Synthetic data are widely used for training modern AI systems. However, their statistical understanding remains limited. It is well recognized in statistics that repeated self-training on synthetic data can amplify errors inherited from pre-trained models, leading to model collapse. Verification plays a crucial role in selecting high-quality synthetic data to help prevent model collapse and improve model performance. We study verified self-training in a linear regression framework, where a pre-trained estimator generates synthetic data with injec