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

2025-11-12 · Hongru Zhao, Jinwen Fu, Tuan Pham arxiv

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.

📄 PDF Abstract BibTeX arXiv:2511.09002

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