When Does Model Collapse Occur in Structured Interactive Learning?

Problem
This preprint addresses a significant gap in the understanding of model collapse within structured interactive learning environments, where generative models are trained on both real and synthetic data produced by other models. Traditional statistical learning assumes that training data is drawn from a target population, a condition violated in this context. The authors highlight that existing literature primarily focuses on single models and their outputs, neglecting the complexities introduced by multi-model interactions. This work aims to formalize and analyze the conditions under which model collapse occurs in these interactive settings.

Method
The authors propose a framework to model interactions between generative models using directed graphs, where nodes represent models and edges denote the flow of synthetic data. They derive a necessary and sufficient condition for model collapse based on the topology of these interaction graphs. The theoretical contributions include finite-sample results for linear regression and asymptotic guarantees for general M-estimators, providing a robust statistical foundation for understanding model performance in interactive learning. The authors conduct extensive numerical experiments to validate their theoretical findings, although specific details regarding the architecture, loss functions, and training compute are not disclosed.

Results
The paper presents empirical results demonstrating the conditions under which model collapse occurs, showing that the interaction graph’s structure significantly influences model performance. While specific numerical results are not detailed in the abstract, the authors indicate that their experiments reveal critical thresholds for model interactions that lead to degradation in generative model performance. Comparisons are made against baseline models trained in isolation, highlighting the detrimental effects of synthetic data propagation in multi-model settings.

Limitations
The authors acknowledge that their analysis is primarily theoretical and may not capture all practical complexities of real-world interactive learning scenarios. They do not address potential scalability issues when applying their framework to larger models or more complex interaction patterns. Additionally, the reliance on directed graphs may oversimplify the dynamics of model interactions, and the lack of detailed experimental setups limits reproducibility.

Why it matters
This work has significant implications for the design and training of generative models in interactive environments, particularly in applications involving collaborative learning or adversarial settings. Understanding the conditions that lead to model collapse can inform strategies to mitigate performance degradation, guiding future research on robust model training methodologies. The findings may also influence the development of new architectures or training protocols that account for the complexities of multi-model interactions, ultimately enhancing the reliability of generative AI systems.

Authors: Yuchen Wu, Kangjie Zhou, Weijie Su
Source: arXiv:2605.20151
URL: https://arxiv.org/abs/2605.20151v1