Convergence and Stability Analysis of Self-Consuming Generative Models with Heterogeneous Human Curation
This work addresses theoretical challenges in generative AI for researchers, offering incremental improvements over prior analyses.
The paper tackles the problem of analyzing the convergence and stability of self-consuming generative models with heterogeneous human curation, providing improved convergence results in non-contractive settings and stability insights.
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.