Modeling generative models as nodes in a directed weighted graph shows cross-model synthetic-data flow jointly sets the convergence threshold and diversity contraction of self-consuming training systems
This work models multiple generative models that consume each other's synthetic data as nodes in a directed weighted graph, derives sufficient conditions for local asymptotic stability of the retraining dynamics via the Jacobian and a comparison matrix, and gives an upper bound on system diversity at the fixed point, showing that stability is jointly governed by local amplification factors and graph propagation while synthetic-data consumption induces a topology-dependent smoothing effect that contracts inter-model heterogeneity; experiments on an 8-mode Gaussian dataset and CIFAR-10 across several generative model classes and interaction topologies align with the theoretical predictions.