分析异质人类偏好下生成模型自迭代的收敛与稳定性问题
Convergence and Stability Analysis of Self-Consuming Generative Models with Heterogeneous Human Curation
- 基于非线性Perron-Frobenius理论研究多轮自重训练动态
- 在传统压缩映射不适用场景中获得收敛性结果
- 揭示模型在不同偏好分布下的稳定与非稳定行为
近年来，自消耗生成模型受到广泛关注。本文研究了一类具有异质人类偏好的自消耗生成模型，该模型是Ferbach等（2024）工作的推广。模型通过真实数据与前一轮合成输出进行多轮重训练。我们利用非线性Perron-Frobenius理论，针对四种不同情形分析了重训练动态的渐近行为。我们的分析优于Ferbach等（2024）的工作，在经典Banach压缩映射方法不适用的情况下仍能提供收敛性结论，并给出了重训练动态的稳定性与非稳定性结果。
原文摘要 · Abstract (English)
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.
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