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

TL;DR

This paper analyzes the convergence and stability of self-consuming generative models with heterogeneous human preferences, extending previous work and providing new theoretical insights into their long-term behavior.

Contribution

It generalizes existing models to include heterogeneous preferences and offers convergence and stability analysis using advanced mathematical techniques.

Findings

Convergence results in regimes where contraction mapping does not apply

Stability and non-stability conditions for retraining dynamics

Improved analysis over previous models in the literature

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.