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This theoretical study demonstrates that generative model collapse during recursive synthetic data retraining can be mitigated by curating outputs based on multiple reward functions rather than a single fixed signal. By formalizing dynamics under heterogeneous preferences, the authors prove that models can converge to a stable distribution preserving diversity through a weighted Nash bargaining solution. This finding offers a rigorous mathematical foundation for maintaining value aggregation in closed-loop synthetic data pipelines without requiring real data injection.
Curated Synthetic Data Doesn't Have to Collapse: A Theoretical Study of Generative Retraining with Pluralistic Preferences
arXiv:2605.07724v2 Announce Type: replace Abstract: Recursive retraining of generative models poses a critical representation challenge: when synthetic outputs are curated based on a fixed reward signal, the model tends to collapse onto a narrow set of outputs that over-optimize that objective. Prior work suggests that such collapse is unavoidable without adding real data into the mix. We revisit this conclusion from an alignment perspective and show that collapse can be mitigated through curation based on multiple reward functions. We formalize the dynamics of recursive training under heterogeneous preferences and prove that, under certain conditions, the model converges to a stable distribution that allocates probability mass across competing high-reward regions. The limiting distribution preserves diversity and provably satisfies a weighted Nash bargaining solution, offering a formal interpretation of value aggregation in synthetic retraining loops.
Abstract:Recursive retraining of generative models poses a critical representation challenge: when synthetic outputs are curated based on a fixed reward signal, the model tends to collapse onto a narrow set of outputs that over-optimize that objective. Prior work suggests that such collapse is unavoidable without adding real data into the mix. We revisit this conclusion from an alignment perspective and show that collapse can be mitigated through curation based on multiple reward functions. We formalize the dynamics of recursive training under heterogeneous preferences and prove that, under certain conditions, the model converges to a stable distribution that allocates probability mass across competing high-reward regions. The limiting distribution preserves diversity and provably satisfies a weighted Nash bargaining solution, offering a formal interpretation of value aggregation in synthetic retraining loops.
Proceedings of the 43rd International Conference on Machine Learning, Seoul, South Korea. PMLR 306, 2026
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
arXiv:2605.07724 [cs.LG]
(or arXiv:2605.07724v2 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2605.07724 Focus to learn more arXiv-issued DOI via DataCite
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