The phenomenon of model collapse, introduced in (Shumailov et al., 2023), refers to the deterioration in performance that occurs when new models are trained on synthetic data generated from previously trained models. This recursive training loop makes the tails of the original distribution disappear, thereby making future-generation models forget about the initial (real) distribution. With the aim of rigorously understanding model collapse in language models, we consider in this paper a statistical model that allows us to characterize the impact of various recursive training scenarios. Specifically, we demonstrate that model collapse cannot be avoided when training solely on synthetic data. However, when mixing both real and synthetic data, we provide an estimate of a maximal amount of synthetic data below which model collapse can eventually be avoided. Our theoretical conclusions are further supported by empirical validations.

模型崩溃是指在使用之前训练的模型生成的合成数据训练新模型时性能下降的现象，本文通过统计模型对各种递归训练情景的影响进行了深入研究，发现当仅使用合成数据进行训练时无法避免模型崩溃，但当混合使用真实数据和合成数据时，我们提供了在合成数据量不超过一定阈值时模型崩溃可以最终避免的估计值，我们的理论结论得到了经验验证的支持。

合成数据训练的糟糕程度：语言模型崩溃的统计分析