October 20, 2025Open Access

A theoretical basis for model collapse in recursive training

Key Points

Model collapse occurs in recursive training, producing distinct outcomes based on sample contributions.
Two different asymptotic behaviours are identified associated with the presence of any external source.
Understanding these behaviours can help refine recursive training methods to mitigate collapse.
This theoretical basis provides insights for future research in generative models and their stability.

Abstract

It is known that recursive training from generative models can lead to the so called `collapse' of the simulated probability distribution. This note shows that one in fact gets two different asymptotic behaviours depending on whether an external source, howsoever minor, is also contributing samples.

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Vivek S. Borkar (Wed,) studied this question.

www.synapsesocial.com/papers/68f6196ee0bbbc94fac3621f — DOI: https://doi.org/10.48550/arxiv.2506.09401

A theoretical basis for model collapse in recursive training

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