This research paper explores the phenomenon of "model collapse," which occurs when AI models trained on synthetic data generated by other AI models start to perform poorly on real-world data. The paper focuses on a supervised regression setting and uses mathematical tools to analyze the impact of synthetic data on model performance. The authors demonstrate that even a small amount of synthetic data can lead to model collapse, even when mixed with real data. The paper examines the relationship between model size and model collapse and explores strategies to mitigate this phenomenon.