Reproduce “A Theoretical Perspective: How to Prevent Model Collapse in Self-consuming Training Loops” on OpenResearch

About this paper

Shi Fu, Yingjie Wang, Yuzhu Chen, Xinmei Tian, Dacheng Tao

This research introduces a theoretical framework for Self-consuming Training Loops (STLs), defining recursive stability and providing the first generalization error bounds for models trained on mixed real and synthetic data. The framework demonstrates that maintaining a non-negligible proportion of real data and ensuring recursive stability are critical to preventing model collapse, particularly when applied to transformer models in in-context learning.

Key insights

• Model collapse in STLs can be prevented if the generative model satisfies recursive stability and a non-negligible, constant proportion of real data is maintained in the training mix.
• Transformers in ICL exhibit recursive stability under certain conditions, and their generalization error within STLs is bounded by terms related to dataset size and the cumulative distribution shift.
• There is a trade-off in synthetic data augmentation: increasing its scale exacerbates cumulative distribution shift but simultaneously decreases generalization error on mixed distributions, with optimal synthetic data size increasing as real data size decreases.

Summary by alphaXiv.