Convergence and Stability Analysis of Self-Consuming Generative Models with Heterogeneous Human Curation

Abstract:Self-consuming generative models have received significant attention over the last few years. In this paper, we study a self-consuming generative model with heterogeneous preferences that is a generalization of the model in Ferbach et al. (2024). The model is retrained round by round using real data and its previous-round synthetic outputs. The asymptotic behavior of the retraining dynamics is investigated across four regimes using different techniques including the nonlinear Perron--Frobenius theory. Our analyses improve upon that of Ferbach et al. (2024) and provide convergence results in settings where the well-known Banach contraction mapping arguments do not apply. Stability and non-stability results regarding the retraining dynamics are also given.

Machine Learning (stat.ML); Machine Learning (cs.LG)

arXiv:2511.09002 [stat.ML]

(or arXiv:2511.09002v3 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2511.09002 Focus to learn more arXiv-issued DOI via DataCite

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